Literatura científica selecionada sobre o tema "Probabilistic number theory"

Abstract While behavioural equivalences among systems of the same type, such as Park/Milner bisimilarity of labelled transition systems, are an established notion, a systematic treatment of relationships between systems of different types is currently missing. We provide such a treatment in the framework of universal coalgebra, in which the type of a system (nondeterministic, probabilistic, weighted, game-based etc.) is abstracted as a set functor: We introduce relational connectors among set functors, which induce notions of heterogeneous (bi)simulation among coalgebras of the respective types. We give a number of constructions on relational connectors. In particular, we identify composition and converse operations on relational connectors; we construct corresponding identity relational connectors, showing that the latter generalize the standard Barr extension of weak-pullback-preserving functors; and we introduce a Kantorovich construction in which relational connectors are induced from relations between modalities. For Kantorovich relational connectors, one has a notion of dual-purpose modal logic interpreted over both system types, and we prove a corresponding Hennessy-Milner-type theorem stating that generalized (bi)similarity coincides with theory inclusion on finitely-branching systems. We apply these results to a number of example scenarios involving labelled transition systems with different label alphabets, probabilistic systems, and input/output conformances.

AbstractA continuous-time Markov chain (CTMC) execution is a continuous class of probability distributions over states. This paper proposes a probabilistic linear-time temporal logic, namely continuous-time linear logic (CLL), to reason about the probability distribution execution of CTMCs. We define the syntax of CLL on the space of probability distributions. The syntax of CLL includes multiphase timed until formulas, and the semantics of CLL allows time reset to study relatively temporal properties. We derive a corresponding model-checking algorithm for CLL formulas. The correctness of the model-checking algorithm depends on Schanuel’s conjecture, a central open problem in transcendental number theory. Furthermore, we provide a running example of CTMCs to illustrate our method.

Abstract Pitting, crevice and stress corrosion cracking are the most damaging corrosion forms of stainless steels in industrial applications. Generally, pitting and crevice susceptibility depends on a variety of factors related to the metal (chemical composition, differences in the metallurgical structure, inclusions), the environment (chloride content, pH, temperature, differential aeration) and the geometry of the system. Due to their unpredictable occurrence, localized corrosion events cannot be explained without using a proper statistical method. In this work a probabilistic approach based on Markov chains for the assessment of pitting and crevice corrosion initiation is proposed. A Markov chain is a stochastic process that undergoes transitions from one state to another through a finite number of possible states, until a so-called "absorbing state” from which the system has no tendency to evolve is attained. Formally, a Markov chain is characterized by a set of states and a transition probability matrix. The model calculates the probability to have pitting (and vice versa to maintain a stable passive condition) involving a large number of operating parameters related to both metal and environment. Experimental tests were carried out to validate the model which requires more accurate investigations.

Abstract A risk based methodology is proposed for the assessment of HTHA (high temperature hydrogen attack). This approach permits the ranking of probability in a semi-quantitative fashion for establishing inspection requirements. The assessment methodology relates the Pv parameter to the operating limits/curves in API 941, where Pv correlates temperature and hydrogen partial to the time for incipient attack1. This, in turn, is correlated to the probability of failure as described on a risk matrix. The results are then used to establish inspection frequency, extent, and priority. The approach outlined here was applied to a C-0.5Mo pressure vessel operating above the carbon steel API 941 curve2. Due to the variable performance of C-0.5Mo steel in hydrogen service there have been a number of unfavorable service experiences with this material, resulting in the removal of the C-0.5Mo curve from API 941. Risk analysis of the pressure vessel evaluated in this study indicated the need for inspection. The inspection for HTHA is traditionally performed when equipment is out of service. However, an on-stream inspection has the advantage of identifying damage before the equipment is shut down and thereby providing adequate lead-time to prepare for replacement or repair. An on-stream inspection program was developed, qualified, and successfully field deployed for the aforementioned vessel, which operates up to 750°F (400°C). The inspection approach relied on the ultrasonic backscatter spectrum analysis method for the base metal inspection and time of flight diffraction – ultrasonic testing (TOFD UT) for weld inspection. This paper will describe the approach and results from the on-stream vessel inspection and a subsequent off stream inspection, which validated the on-stream results.

Abstract Intelligent pig inspections between 2000 and 2003 revealed severe corrosion damage in a number of Main Oil Line pipeline sections to such level that continued operation was jeopardized. Replacement of 3 Main Oil Line sections was planned for 2004 because of integrity problems. In order to overcome the direct integrity threat, specialized defect assessment was introduced in 2002 to reduce the conservatism in the defect assessment with respect to defect interaction rules. Continued operation could be justified by this special analysis. In 2003, a special hydraulic analysis applying the "Head versus Distance" methodology was introduced to review the pressure safeguarding of the system, which allowed derating of one of the Main Oil Line sections as such increasing the corrosion tolerance of the section. In addition a new risk based “Inspect- Repair” strategy was developed to manage the integrity of the corroding pipelines longer-term. This strategy was incorporated in Company’s Pipe-RBA (Risk Based Assessment) methodology and although it is not based on a probabilistic assessment, it does take into account the probabilistic nature of corrosion growth. Robust permanent repair strategies were developed for both internal and external defects including the quality control aspects of applying the repairs. As a result of all this work, the life of 2 lines is extended by at least 10 years but possibly indefinitely and the life of 1 line is extended by at least 7 years. Total replacement cost of the 3 lines is 71 million $. This paper outlines the risk based methodologies used and their application to two line sections.

Abstract From the beginning, engineers have focused on the special case of determinism in the design process, and an enormous methodology has been developed to support this approach. Today, however, customers are demanding greater reliability and are imposing greater penalties for failure. In order to achieve higher reliability, and in order to assess the risk of failure, probabilistic approaches will almost certainly have to be employed. While designers have always used probability in their work, it has usually been done with risk represented in a single factor of safety. This paper focuses on the application of probability theory to the design of multi-degree of freedom systems that are subjected to a number of discreet excitation frequencies. Problems of this nature are often encountered in rotating machines where the excitation frequencies are multiples of the speed of rotation. In a previous paper (Pigott, 1996), only variability in the system natural frequencies was considered, and the probability of exceeding a certain vibratory stress was determined. It was shown that, at the reliability levels of interest, it is necessary to consider multiple mode contributions to the total vibratory stress. In this paper, the previous approach is extended to include variability in the magnitude of the excitation force, system damping, and system fatigue strength leading to the determination of a total probability of failure due to high cycle fatigue. The results of applying the deterministic analysis, the first level of probabilistic analysis (Pigott, 1996) and the full probabilistic analysis are presented for a sample system. The benefits from using the probabilistic approach for component design are also discussed.

The image of a natural scene can be considered a product of reflectance and effective illumination functions. One goal of image understanding is the estimation of the reflectance and illumination from image luminance data. Human observers are remarkably good at inferring reflectance changes from an image. One well-known aspect of this ability is lightness constancy. However, because there are two unknowns for every data point in the image, this problem is ill-posed, and it does not have a unique solution without prior constraints on the class of reflectance and illumination functions. We use Markov random fields to model and thereby constrain the class of reflectance and illumination functions. Our computational goal is taken to be the maximization of the posterior distribution of the reflectance and illumination conditional on the image. This goal is achieved using stochastic relaxation. This approach provides a general framework for quantifying the computational theory apart from specific algorithmic implementations for a number of problems of early vision.

In multi-agent belief fusion, there is increasing interest in results and methods from social choice theory. As a theoretical cornerstone, the Condorcet Jury Theorem (CJT) states that given a number of equally competent, independent agents where each is more likely to guess the true out of two alternatives, the chances of determining this objective truth by majority voting increase with the number of participating agents, approaching certainty. Past generalizations of the CJT have shown that some of its underlying assumptions can be weakened. Motivated by requirements from practical belief fusion scenarios, we provide a significant further generalization that subsumes several of the previous ones. Our considered setting simultaneously allows for heterogeneous competence levels across the agents (even tolerating entirely incompetent or even malicious voters), and voting for any number of alternatives from a finite set. We derive practical lower bounds for the numbers of agents needed to give probabilistic guarantees for determining the true state through approval voting. We also demonstrate that the non-asymptotic part of the CJT fails in our setting for arbitrarily high numbers of voters.

Flexible marine risers are compliant to external forces from waves, current and platform motions, and clashing between risers is an important concern. In deepwater developments where the number of connected risers is large, it is not economical to space them too far apart. In this regard, it is necessary to establish the probability of riser clashing throughout the service life; however, at present there appears to be no systematic procedure for assessing this risk. This paper presents a novel procedure for estimating the probability of riser clashing based on post-processing results obtained from time domain simulations of flexible risers subjected to random wave loads. First, an efficient technique is employed to sieve out critical pairs among riser elements. From these element pairs, the time history of a normalized clearance parameter is derived from the nodal displacements of the elements. Subsequently, the mean up-crossing rate of this parameter is extracted and extrapolated to the threshold of clashing using extreme value theory. As this method is still in its early developmental stage, critical effects such as vortex-induced vibrations and wake interference will not be considered in the present work.

Field measurements of the steamside oxide thickness for high temperature (> 850F) boiler tubing subject to the accumulation of creep damage often are made to support deterministic assessments of the remaining life. Most often, these inspections are undertaken to understand the condition of the tubing at some particular location along a circuit, often as a result of a tube failure. The life assessment is based on relationships that have been developed between oxide growth kinetics and temperature. Unfortunately, because of variability in the oxide-temperature relationships reflecting different original data sets, and because of the inherent uncertainty in materials properties where heat-specific test data is not available, there typically exists a broad range of uncertainty in the deterministic assessment results. Large utility-type boilers typically contain a number of high temperature sections, including various stages of superheat and reheat, each of which will contain miles of tubing. Since the temperature derived from an oxide thickness measurement is relevant only to the specific location where the measurement was made, the deterministically derived life calculation is also specific to that location. As a result, the attempt to draw conclusions regarding the condition of an entire superheater or reheater section from measurements made at only one or two locations in those sections is fraught with difficulties. It is for this reason that the Probabilistic Gas Touched Length Analysis model has been developed. This model makes it possible to calculate creep damage accumulation/remaining life at any point along the steam path. Oxide thickness data and operating data are the primary operating inputs into the model, which performs heat transfer calculations at user-defined locations along the length of the tube circuit. The model applies statistical methods to evaluate variations in operating conditions as well as in physical and mechanical properties using a Monte Carlo simulation to generate values for the probability of failure at selected locations. This paper will discuss the limitations of the existing approach to estimating the remaining life of high temperature boiler tubing and present the underpinning theory of the gas touched length analysis model. A case study showing the analysis results is included.

Over the past decade, the use of Probabilistic Seismic Hazard Analysis (PSHA) to assess seismic hazards has expanded, leading to the creation of a number of new PSHA computer codes throughout the industry. Additionally, recent seismic source and ground-motion characterization studies have led to more complex source and ground-motion models, which necessitate implementation in PSHA codes. This project was undertaken to update previous PSHA computer code verification efforts by running an expanded set of verification tests on codes currently in use for PSHA calculations. Following an announcement to the community, fifteen owners of PSHA codes from private consulting companies, academic institutions, risk analysis firms, and government agencies participated in the verification project by running verification tests on their own codes. The project included three sets of tests that increased in complexity from the first test in Set 1 to the last test in Set 3. Over the course of the project the group held ten meetings to discuss and finalize the results. Tests were often re-run several times before the results for all codes were finalized. This report documents the specifications and benchmark answers for the verification tests. Common issues and programming errors are also summarized, along with standard modeling approaches and key discussion points from the meetings. Where differences in modeling approaches lead to differences in reported hazard, those different modeling approaches are described. Through participation in the project, code owners verified the primary functions of their codes as benchmark answers were reached. The PSHA codes developed in the future can be verified by running the tests and comparing the results to the benchmark answers documented in this report. Note: the scope of this project is PSHA computer code verification. This project does not make recommendations on how to model earthquake scenarios from the specified source-characterization or ground-motion characterization inputs.

Executive Summary “People don’t understand probabilities” – or do they? Weather forecasting science has long been developing ensemble forecasts as a way to improve forecast capability and provide better information to support users’ decisions. The science is well proven and, indeed, the Met Office will soon move to an ensemble-only NWP (Numerical Weather Prediction) system. Ensemble forecasts can be used in a number of ways, but fundamentally they provide a probabilistic picture of the weather forecast including a most likely outcome and information on the confidence, uncertainty or risks associated with forecast outcomes. In order to pull through the full benefits of this information it is important to communicate this information effectively to users so that they can make appropriate risk-based decisions. There is a widely-held belief that people will find probabilistic information hard to understand or make use of, which provides a significant obstacle to communicating it. This challenge for ensemble or probabilistic forecasts has long been recognised and there has been extensive research conducted into effective communication and people’s understanding of such forecasts, including several papers led or sponsored by the Met Office. This paper offers a review of that research to help guide future communications of forecasts. The overwhelming and consistent conclusion found in the literature is that people do understand the probabilistic information and make better decisions when presented with it, provided that the information is presented appropriately. Key conclusions include: • Nearly all of the studies indicate that people make better decisions, have more trust in information, and/or display more understanding of forecast information when forecasters use probability information in place of deterministic statements. • Providing additional information on uncertainty does not lead to confusion and misinterpretation compared to simple deterministic forecasts. • The inclusion of a numerical probability (e.g. 30%) alongside a visual or worded description can greatly help with correct interpretation; using both forms helps ensure that both more and less numerate individuals will understand the message. • Careful choice of language helps to promote understanding e.g. some people may be put off by “30% probability” which they consider to be mathematical, but are quite comfortable with “30% chance” and interpret it correctly. • It is important clearly define the events to which probabilities apply, and the way in which forecasters frame messages can influence how audiences interpret risks. Overall, the literature review provides strong support for communicating probabilistic information to forecast users, including the general public. It does not support the idea that people’s understanding should be a barrier to communicating such information. While not every single person will understand or take full advantage of the additional information, most people will benefit and make better decisions as a result. The review also offers a number of suggestions for optimising effective communication.

This technical paper argues that Monte Carlo risk analysis offers a more comprehensive and informative way to look at project risk ex-ante than the traditional (and often arbitrary), one-influence-at-atime sensitivity analysis approach customarily used in IDB analyses of economic feasibility. The case for probabilistic risk analysis is made using data from a project for cleaning up the Tietê river in São Paulo, Brazil. A number of ways to handle uncertainty about benefits are proposed, and their implications for the project acceptance decision and the consequent degree of presumed project risk are explained and illustrated.

Key Points This report presents scenarios of adolescent contraceptive use through 2030 to highlight the potential impact and costs associated with overall increased contraceptive use among adolescents and an increased use of long-acting, reversible contraceptives (LARCs), specifically. Under a scenario that assumes the most likely level of modern contraceptive use to be reached in a particular year (median values of probabilistic projections), the number of adolescent women using modern contraceptives in developing regions would reach 19.8 million in 2030, and 57% of adolescent women would have their need for modern contraception met. The total annual cost of services in 2030 for the projected 19.8 million modern method users would be an estimated $310 million. The cost would be lower, at $275 million, if 20% of adolescent women using short-acting methods were to choose LARCs. An estimated 7.1 million unintended pregnancies would be averted under this scenario. Because LARCs are highly effective, a shift toward use of these methods would avert an additional 300,000 unintended pregnancies. Under a scenario with accelerated growth in modern contraceptive use among adolescent women in developing regions, the number of modern method users would reach 27.1 million in 2030, and the proportion of adolescent women whose need for modern contraception would be met would rise to 79%. Contraceptive services for the 27.1 million modern method users in 2030 would cost an estimated $412 million. The cost would drop to $365 million under an assumption of increased LARC use. In 2030, an estimated 9.6 million unintended pregnancies would be averted under this accelerated growth scenario, and an additional 400,000 unintended pregnancies would be averted with a shift to LARC use.

This report is one of a series of reports documenting the methods and findings of a multi-year, multi-disciplinary project coordinated by the Pacific Earthquake Engineering Research Center (PEER) and funded by the California Earthquake Authority (CEA). The overall project is titled “Quantifying the Performance of Retrofit of Cripple Walls and Sill Anchorage in Single-Family Wood-Frame Buildings,” henceforth referred to as the “PEER–CEA Project.” The overall objective of the PEER–CEA Project is to provide scientifically based information (e.g., testing, analysis, and resulting loss models) that measure and assess the effectiveness of seismic retrofit to reduce the risk of damage and associated losses (repair costs) of wood-frame houses with cripple wall and sill anchorage deficiencies as well as retrofitted conditions that address those deficiencies. Tasks that support and inform the loss-modeling effort are: (1) collecting and summarizing existing information and results of previous research on the performance of wood-frame houses; (2) identifying construction features to characterize alternative variants of wood-frame houses; (3) characterizing earthquake hazard and ground motions at representative sites in California; (4) developing cyclic loading protocols and conducting laboratory tests of cripple wall panels, wood-frame wall subassemblies, and sill anchorages to measure and document their response (strength and stiffness) under cyclic loading; and (5) the computer modeling, simulations, and the development of loss models as informed by a workshop with claims adjustors. This report is a product of Working Group 3 (WG3), Task 3.1: Selecting and Scaling Ground-motion records. The objective of Task 3.1 is to provide suites of ground motions to be used by other working groups (WGs), especially Working Group 5: Analytical Modeling (WG5) for Simulation Studies. The ground motions used in the numerical simulations are intended to represent seismic hazard at the building site. The seismic hazard is dependent on the location of the site relative to seismic sources, the characteristics of the seismic sources in the region and the local soil conditions at the site. To achieve a proper representation of hazard across the State of California, ten sites were selected, and a site-specific probabilistic seismic hazard analysis (PSHA) was performed at each of these sites for both a soft soil (Vs30 = 270 m/sec) and a stiff soil (Vs30=760 m/sec). The PSHA used the UCERF3 seismic source model, which represents the latest seismic source model adopted by the USGS [2013] and NGA-West2 ground-motion models. The PSHA was carried out for structural periods ranging from 0.01 to 10 sec. At each site and soil class, the results from the PSHA—hazard curves, hazard deaggregation, and uniform-hazard spectra (UHS)—were extracted for a series of ten return periods, prescribed by WG5 and WG6, ranging from 15.5–2500 years. For each case (site, soil class, and return period), the UHS was used as the target spectrum for selection and modification of a suite of ground motions. Additionally, another set of target spectra based on “Conditional Spectra” (CS), which are more realistic than UHS, was developed [Baker and Lee 2018]. The Conditional Spectra are defined by the median (Conditional Mean Spectrum) and a period-dependent variance. A suite of at least 40 record pairs (horizontal) were selected and modified for each return period and target-spectrum type. Thus, for each ground-motion suite, 40 or more record pairs were selected using the deaggregation of the hazard, resulting in more than 200 record pairs per target-spectrum type at each site. The suites contained more than 40 records in case some were rejected by the modelers due to secondary characteristics; however, none were rejected, and the complete set was used. For the case of UHS as the target spectrum, the selected motions were modified (scaled) such that the average of the median spectrum (RotD50) [Boore 2010] of the ground-motion pairs follow the target spectrum closely within the period range of interest to the analysts. In communications with WG5 researchers, for ground-motion (time histories, or time series) selection and modification, a period range between 0.01–2.0 sec was selected for this specific application for the project. The duration metrics and pulse characteristics of the records were also used in the final selection of ground motions. The damping ratio for the PSHA and ground-motion target spectra was set to 5%, which is standard practice in engineering applications. For the cases where the CS was used as the target spectrum, the ground-motion suites were selected and scaled using a modified version of the conditional spectrum ground-motion selection tool (CS-GMS tool) developed by Baker and Lee [2018]. This tool selects and scales a suite of ground motions to meet both the median and the user-defined variability. This variability is defined by the relationship developed by Baker and Jayaram [2008]. The computation of CS requires a structural period for the conditional model. In collaboration with WG5 researchers, a conditioning period of 0.25 sec was selected as a representative of the fundamental mode of vibration of the buildings of interest in this study. Working Group 5 carried out a sensitivity analysis of using other conditioning periods, and the results and discussion of selection of conditioning period are reported in Section 4 of the WG5 PEER report entitled Technical Background Report for Structural Analysis and Performance Assessment. The WG3.1 report presents a summary of the selected sites, the seismic-source characterization model, and the ground-motion characterization model used in the PSHA, followed by selection and modification of suites of ground motions. The Record Sequence Number (RSN) and the associated scale factors are tabulated in the Appendices of this report, and the actual time-series files can be downloaded from the PEER Ground-motion database Portal (https://ngawest2.berkeley.edu/)(link is external).

Aging infrastructure within the US Department of Energy (DOE) and the National Nuclear Security Administration (NNSA) nuclear facilities poses a major challenge to their resiliency against natural phenomenon hazards. Examples of mission-critical facilities located in regions of high seismicity can be found at a number of NNSA sites including Lawrence Livermore National Laboratory, Los Alamos National Laboratory, and the Nevada National Security Site. Most of the nation’s currently operating nuclear facilities have already reached their operating lifetime, and most currently operating nuclear power plants (NPPs) have already reached the extent of their operating license period. While the domestic demand for electrical energy is expected to grow, if currently operating NPPs do not extend their operations and additional plants are not built quickly enough to replace them, the total fraction of electrical energy generated from carbon-free nuclear power will rapidly decline. The decision to extend operation is ultimately an economic one; however, economics can often be improved through technical advancements (McCarthy et al. 2015) and research and development (R&D) activities. Similarly, the operating lifetime of the current DOE- and NNSA-owned critical infrastructure can be extended using the Probabilistic Risk Assessment (PRA) framework to systematically identify the risk associated with designing and operating existing facilities and building new ones. Using this framework consists of several steps, including (1) system analysis considering the interaction between components, such as evaluating the soil-foundation-structure system response; and (2) assessment of areas of uncertainty. Both of these steps are essential to assessing and reducing risks to the DOE and NNSA nuclear facilities. While the risks to the DOE’s facilities are primarily due to natural hazard phenomena, data from large-scale tests of the soil-foundation-structural system response to seismic shaking is currently lacking. This workshop aimed to address these key areas by organizing an international workshop focused on advancing the seismic safety of nuclear facilities using large-scale shake table testing. As a result, this workshop, which was held virtually, brought together a select group of international experts in large-scale shake table testing from the U.S., Japan, and Europe to discuss state-of-the-art experimental techniques and emerging instrumentation technologies that can produce unique experimental data to advance knowledge in natural hazards that impact the safety of the DOE’s nuclear facilities. The generated experimental data followed by research and development activities will ultimately result in updates to ASCE 4-16, one of the primary design guides for DOE nuclear facilities per DOE-STD-1020-2016. The ultimate objective of the workshop was to develop a “road map” for the future experimental campaign and innovative instrumentations using the newly constructed DOE-funded large-scale shake table facility at the University of Nevada, Reno (UNR) as well as other large-scale shake table testing facilities. This new facility resulted from a collaborative project engagement between UNR and Lawrence Berkeley National Laboratory. (LBNL). This report summarizes the proceedings of the workshop and highlights the key outcomes from presentations and discussions.

The Genetic Technology (Precision Breeding) Act (England) aims to develop a science-based process for the regulation and authorisation of precision bred organisms (PBOs). PBOs are created by genetic technologies but exhibit changes which could have occurred through traditional processes. This current review, commissioned by the Food Standards Agency (FSA), aims to clarify existing terminologies, explore viable methods for the detection, identification, and quantification of products of precision breeding techniques, address and identify potential solutions to the analytical challenges presented, and provide recommendations for working towards an infrastructure to support detection of precision bred products in the future. The review includes a summary of the terminology in relation to analytical approaches for detection of precision bred products. A harmonised set of terminology contributes towards promoting further understanding of the common terms used in genome editing. A review of the current state of the art of potential methods for the detection, identification and quantification of precision bred products in the UK, has been provided. Parallels are drawn with the evolution of synergistic analytical approaches for the detection of Genetically Modified Organisms (GMOs), where molecular biology techniques are used to detect DNA sequence changes in an organism’s genome. The scope and limitations of targeted and untargeted methods are summarised. Current scientific opinion supports that modern molecular biology techniques (i.e., quantitative real-time Polymerase Chain Reaction (qPCR), digital PCR (dPCR) and Next Generation Sequencing (NGS)) have the technical capability to detect small alterations in an organism’s genome, given specific prerequisites of a priori information on the DNA sequence of interest and of the associated flanking regions. These techniques also provide the best infra-structure for developing potential approaches for detection of PBOs. Should sufficient information be known regarding a sequence alteration and confidence can be attributed to this being specific to a PBO line, then detection, identification and quantification can potentially be achieved. Genome editing and new mutagenesis techniques are umbrella terms, incorporating a plethora of approaches with diverse modes of action and resultant mutational changes. Generalisations regarding techniques and methods for detection for all PBO products are not appropriate, and each genome edited product may have to be assessed on a case-by-case basis. The application of modern molecular biology techniques, in isolation and by targeting just a single alteration, are unlikely to provide unequivocal evidence to the source of that variation, be that as a result of precision breeding or as a result of traditional processes. In specific instances, detection and identification may be technically possible, if enough additional information is available in order to prove that a DNA sequence or sequences are unique to a specific genome edited line (e.g., following certain types of Site-Directed Nucelase-3 (SDN-3) based approaches). The scope, gaps, and limitations associated with traceability of PBO products were examined, to identify current and future challenges. Alongside these, recommendations were made to provide the infrastructure for working towards a toolkit for the design, development and implementation of analytical methods for detection of PBO products. Recognition is given that fully effective methods for PBO detection have yet to be realised, so these recommendations have been made as a tool for progressing the current state-of-the-art for research into such methods. Recommendations for the following five main challenges were identified. Firstly, PBOs submitted for authorisation should be assessed on a case-by-case basis in terms of the extent, type and number of genetic changes, to make an informed decision on the likelihood of a molecular biology method being developed for unequivocal identification of that specific PBO. The second recommendation is that a specialist review be conducted, potentially informed by UK and EU governmental departments, to monitor those PBOs destined for the authorisation process, and actively assess the extent of the genetic variability and mutations, to make an informed decision on the type and complexity of detection methods that need to be developed. This could be further informed as part of the authorisation process and augmented via a publicly available register or database. Thirdly, further specialist research and development, allied with laboratory-based evidence, is required to evaluate the potential of using a weight of evidence approach for the design and development of detection methods for PBOs. This concept centres on using other indicators, aside from the single mutation of interest, to increase the likelihood of providing a unique signature or footprint. This includes consideration of the genetic background, flanking regions, off-target mutations, potential CRISPR/Cas activity, feasibility of heritable epigenetic and epitranscriptomic changes, as well as supplementary material from supplier, origin, pedigree and other documentation. Fourthly, additional work is recommended, evaluating the extent/type/nature of the genetic changes, and assessing the feasibility of applying threshold limits associated with these genetic changes to make any distinction on how they may have occurred. Such a probabilistic approach, supported with bioinformatics, to determine the likelihood of particular changes occurring through genome editing or traditional processes, could facilitate rapid classification and pragmatic labelling of products and organisms containing specific mutations more readily. Finally, several scientific publications on detection of genome edited products have been based on theoretical principles. It is recommended to further qualify these using evidenced based practical experimental work in the laboratory environment. Additional challenges and recommendations regarding the design, development and implementation of potential detection methods were also identified. Modern molecular biology-based techniques, inclusive of qPCR, dPCR, and NGS, in combination with appropriate bioinformatics pipelines, continue to offer the best analytical potential for developing methods for detecting PBOs. dPCR and NGS may offer the best technical potential, but qPCR remains the most practicable option as it is embedded in most analytical laboratories. Traditional screening approaches, similar to those for conventional transgenic GMOs, cannot easily be used for PBOs due to the deficit in common control elements incorporated into the host genome. However, some limited screening may be appropriate for PBOs as part of a triage system, should a priori information be known regarding the sequences of interest. The current deficit of suitable methods to detect and identify PBOs precludes accurate PBO quantification. Development of suitable reference materials to aid in the traceability of PBOs remains an issue, particularly for those PBOs which house on- and off-target mutations which can segregate. Off-target mutations may provide an additional tool to augment methods for detection, but unless these exhibit complete genetic linkage to the sequence of interest, these can also segregate out in resulting generations. Further research should be conducted regarding the likelihood of multiple mutations segregating out in a PBO, to help inform the development of appropriate PBO reference materials, as well as the potential of using off-target mutations as an additional tool for PBO traceability. Whilst recognising the technical challenges of developing and maintaining pan-genomic databases, this report recommends that the UK continues to consider development of such a resource, either as a UK centric version, or ideally through engagement in parallel EU and international activities to better achieve harmonisation and shared responsibilities. Such databases would be an invaluable resource in the design of reliable detection methods, as well as for confirming that a mutation is as a result of genome editing. PBOs and their products show great potential within the agri-food sector, necessitating a science-based analytical framework to support UK legislation, business and consumers. Differentiating between PBOs generated through genome editing compared to organisms which exhibit the same mutational change through traditional processes remains analytically challenging, but a broad set of diagnostic technologies (e.g., qPCR, NGS, dPCR) coupled with pan-genomic databases and bioinformatics approaches may help contribute to filling this analytical gap, and support the safety, transparency, proportionality, traceability and consumer confidence associated with the UK food chain.