New designs of water-cooled reactors that include thermal-hydraulics systems undergo safety analysis during the licensing process. For economic reasons and safety concerns, systems are firstly tested on reduced scale test facilities. A proper scaling ensures that dominant thermalhydraulics safety-related phenomena are captured, even though unavoidable scale distortions occur. Some existing scaling methods, based on prior knowledge of the physical phenomena at stake, can quantify such distortions. They are however limited when the phenomena are non-linear and coupled, or even not formalized as an equation. Dimensionless numbers play a central role in scaling techniques as their scale invariant properties help preserve similarities between reactor and test facilities. Building on this principle, this paper proposes a data driven alternative to traditional scaling techniques. From a dataset of physical variables describing the phenomenon of interest, the method identifies a governing law that captures the dominant safety related phenomenon. This governing law is expressed in terms of dimensionless numbers, which are physically meaningful combinations of dimensional variables and are automatically inferred by the algorithm. Based on a clear mathematical formulation, the proposed data driven method combines advanced regression analysis with the constrained optimization of a cross validation based objective function. Two variants are presented: one assuming that the output of the nondimensional governing law is known, and an extension in which this output is estimated. Both variants identify the dominant input dimensionless number as well as the explicit form of the governing law. As a proof of concept, the method is tested on a simulated dataset representative of single-phase natural circulation in a passive heat removal system.
Ethereum, developed by Vitalik Buterin in 2013, has significantly advanced blockchain technology through smart contracts and ERC-20 token standards. This study examines the impact of Ethereum on ERC-20 tokens using Long Short-Term Memory (LSTM) and Convolutional Neural Networks (CNN) models. For this purpose, LSTM and CNN models were trained using Ethereum data and then employed to predict ERC-20 token prices. According to the study's results, the LSTM model achieved high accuracy rates for LINK, MATIC, and UNI tokens but performed poorly in predicting RNDR token prices. The CNN model provided the highest accuracy for LINK tokens and yielded successful results in predicting RNDR token prices. However, the CNN model showed lower performance for MATIC and UNI tokens than the LSTM model. These findings indicate that both LSTM and CNNmodels significantly impact the prediction of Ethereum's ERC-20 token price dynamics. The variability in model performances across tokens highlights the influence of market dynamics and liquidity levels. In light of these differences, the study emphasizes the importance of selecting the model based on the token's characteristics and market conditions.
ĐНокŃĐ°Đ˝Đ´Ń ĐŃСноŃОв, Anton Yezhov, Kateryna Kuznetsova, Oleksandr Domin
This study presents a comprehensive theoretical and empirical analysis of Patricia tries, the fundamental data structure underlying Ethereum's state management system. We develop a probabilistic model characterizing the distribution of path lengths in Patricia tries containing random Ethereum addresses and validate this model through extensive computational experiments. Our findings reveal the logarithmic scaling of average path lengths with respect to the number of addresses, confirming a crucial property for Ethereum's scalability. The study demonstrates high precision in predicting average path lengths, with discrepancies between theoretical and experimental results not exceeding 0.01 across tested scales from 100 to 100,000 addresses. We identify and verify the right-skewed nature of path length distributions, providing insights into worst-case scenarios and informing optimization strategies. Statistical analysis, including chi-square goodness-of-fit tests, strongly supports the model's accuracy. The research offers structural insights into node concentration at specific trie levels, suggesting avenues for optimizing storage and retrieval mechanisms. These findings contribute to a deeper understanding of Ethereum's fundamental data structures and provide a solid foundation for future optimizations. The study concludes by outlining potential directions for future research, including investigations into extreme-scale behavior, dynamic trie performance, and the applicability of the model to non-uniform address distributions and other blockchain systems.
A common aim of epidemiological research is to estimate the association between a particular exposure and a particular outcome, with the aim to better understand potential causal mechanisms behind this association. In 2020, Li et al1 proposed a method they called âInference about causation from examination of familial confoundingâ (abbreviated ICE FALCON), which uses twin data (or, more generally, data on related individuals) to assess whether an association is due to a causal effect of the exposure, reverse causation, familial confounding, or a mix of the three. In brief, this method requires the analyst to first regress an individualâs outcome on her own exposure, then on her twinâs exposure, and then finally on her own exposure and her twinâs exposure simultaneously. Li et al1 argued that by examining the pattern of the estimated regression coefficients the analyst could infer the true mechanism that generated the data, and claimed the method was analogous to Mendelian randomization (MR), but with certain additional benefits. Since this methodological paper was published it has been cited 31 times according to Google Scholar, and in a later paper, Li et al2 claimed that the ICE FALCON method has âprovided causal evidence for numerous exposure and outcomesâ, citing 14 publications for this claim. In this cautionary note, we argue that the ICE FALCON method is based on highly unrealistic assumptions that were not clearly stated by Li et al,1 and several statistical errors. The note is organized as follows. We first review the key elements of the ICE FALCON method. Next, we lay out our critique against the method. We finally consider the real data example given by Li et al,1 and argue that far less can be said about underlying mechanisms in this example than promised by the ICE FALCON method. Throughout, we ignore sampling variability and focus on the large sample behaviour of estimated regression coefficients. We adopt the notation by Li et al.1 Let Xself and Yself be the exposure and outcome for a particular individual, and Xco-twin and Yco-twin be the exposure and outcome for that individualâs co-twin. Li et al1 considered the possible mechanisms illustrated by the causal diagrams in Figure 1 (identical to their Figure 1). In these diagrams, SXY is the set of family-constant confounders for X and Yâ , SX is the set of family-constant factors that influence X but not Yâ , and SY is the set of family-constant factors that influence Y but not Xâ . Finally, U is the set of unmeasured within-individual confounders, i.e. the confounders that may have different values for the two twins in a pair. Apart from unmeasured within-individual confounding, in Figure 1a the statistical association between X and Y is due to familial confounding, in Figure 1b it is due to causation, and in Figure 1c it is due to reverse causation. Figure 1d illustrates a mixture of familial confounding and causation, and Figure 1e illustrates a mixture of familial confounding and reverse causation. Like Li et al,1 we first restrict attention to the three simpler scenarios in Figure 1a-c, and later comment on mixtures of these. Possible mechanisms underlying a statistical association between X and Yâ , as proposed by Li et al1 Note that, in Models 1â3, the intercepts Îąâ , ιⲠand Îąâł are generally different, as well as the coefficients βself and βselfâ˛â , and the coefficients βco-twin and βco-twinâ˛â . Note also that, since X and Y are available for both twins in each pair, each twin contributes as both âselfâ and âco-twinâ to the fitted models. Li et al1 argued that the mechanisms in Figure 1a-c imply the coefficient patterns summarized in Table 1 (identical to their Table 1), where ĎX and ĎY are the within-pair correlations in X and Yâ , respectively. Since each pattern (e.g. column in the table) is unique, they concluded that the estimated regression coefficients could be used to distinguish between these three mechanisms. For instance, if we observe that βselfâ˛=βself and βco-twinâ˛=0â , then, according to Li et al,1 we can rule out both familial confounding and reverse causation, since this coefficient pattern is unique for causation. Unique regression coefficient patterns implied by the three mechanisms in Figure 1, according to Li et al1 Unique regression coefficient patterns implied by the three mechanisms in Figure 1, according to Li et al1 Li et al1 provided both graphical arguments (in their main text) and mathematical proofs (in their Supplementary material) for the coefficient patterns in Table 1. However, there are two important problems with these arguments and proofs: (1) they ignore the influence of unmeasured within-individual confounders, and (2) they conflate statistical conditioning with accounting for correlated observations. Below, we discuss these problems in more detail. In the Supplementary material we show that, when these issues are acknowledged, there is no guarantee that the mechanisms in Figure 1a-c will produce distinct coefficient patterns. In particular, we give numerical examples where all three mechanisms result in identical coefficient patterns. In virtually all real family studies, unmeasured within-individual confounders U will be present. Or stated differently: there are likely to exist confounders which are not identically shared by the twins, and which we cannot perfectly adjust for in our regression models. Depending on the context, these may have larger or smaller magnitude than the familial confounders SXYâ , and may affect X and Y in the same or opposite direction. We have previously shown that unmeasured within-individual confounders have important consequences for the interpretation of sibling comparison studies, since their effect will be numerically different in the full cohort and when conditioning on the sibling pair.3 However, Li et al1 effectively ignored unmeasured within-individual confounders when deriving Table 1. For instance, they wrote (page 1261, second column) âIf there is familial confounding only ⌠(Figure 1a), there will be associations between⌠Yself and Xco-twin (â βco-twinâ , Model 2). Adjusting for Xself (Model 3), there will still be a conditional association between Yself and Xco-twin (â βco-twinâ˛â ), but it will be attenuated towards the null compared with βco-twinâ. This conclusion is not generally valid when Uself is present, since adjusting for Xself then opens the path YselfâUselfâXselfâSXâXco-twin at which Xself is a collider, which may inflate the association between Yself and Xco-twinâ . As another example, they wrote: âIf there is a causal effect from X to Y only (Figure 1b), ⌠the conditional [on Xself] association between Yself and Xco-twin (â βco-twinâ˛â ) will be nullâŚâ This conclusion is also invalid when Uself is present, since adjusting for Xself then again opens the aforementioned path, which will induce a statistical association between Yself and Xco-twinâ . Similar issues apply to several of the other coefficient patterns in Table 1. In their Supplementary material, Li et al1 explicitly articulated the assumption of no unmeasured within-individual confounders. However, they did this by writing âFor simplicity we assume that ⌠there was no within-individual confoundingâ (italics added), without commenting on the implausibility of this assumption in real studies or acknowledging that the ICE FALCON method is invalid when the assumption is violated. This gives the reader the misleading impression that the assumption was made purely for mathematical convenience, and that it is not required by the ICE FALCON method. This impression is further enforced by the fact that, in the main text of the paper, the assumption is not mentioned at all; on the contrary, all the causal diagrams in the paper include within-individual confounders, and the text repeatedly refer to these as if they are not assumed absent. For instance, when comparing the ICE FALCON method to MR, they state (in their Table 4), as a relative advantage of the former, that âXco-twin is theoretically unrelated to unmeasured confounders specific to an individual only [italics added]â. We have not scrutinized all 14 papers that Li et al2 cite for using the ICE FALCON method, but several of them appear to have entirely missed the crucial role of unmeasured within-individual confounders for the method. For instance, Zheng et al4 studied the association between socio-economic status and obesity among adult monozygotic and dizygotic twins, which may clearly suffer from unmeasured within-individual confounding by various life-style and (for dizygotic twins) genetic factors. The authors indeed included within-individual confounders in their causal diagrams (identical to Figure 1a-c); however, they then proceeded by analysing data with the ICE FALCON method as if unmeasured within-individual confounders were absent altogether. Then, Model 2* would still produce incorrect standard errors if fitted with ordinary linear regression instead of a GEE, since each twin contributes as both âselfâ and âco-twinâ to the model. This conceptual mistake led Li et al1 to several incorrect conclusions about the coefficient patterns in Table 1. For instance, they wrote âIf there is a causal effect from Y to X only (Figure 1c), ⌠[then in] Model 2, there is no open path between Yself and Xco-twinâthe path through SY is closed due to the fact that Yco-twin is conditioned onâ. Presumably, they here referred to the path YselfâSYâYco-twinâXco-twinâ , which would indeed be closed if Yco-twin were conditioned on. However, since fitting Model 2 with a GEE does not condition on Yco-twin the path remains open. Ironically, if Yco-twin were truly conditioned on, then the path YselfâSYâYco-twinâUco-twinâXco-twin at which Yco-twin is a collider would be open instead. Curiously, whereas Li et al1 claimed that Model 2 becomes conditioned on Yco-twin when accounting for correlated observations, they did not make such claims for Models 1 and 3, whereas, in fact, the issue of correlated observations is equally present for these models. Thus, by their (incorrect) logic, Models 1 and 3 would also be conditioned on Yco-twin when fitted with a GEE. In real scenarios, the true mechanism behind an observed association will likely be a mixture of confounding and causation, or between confounding and reverse causation, as in Figure 1d and e, respectively. For such scenarios, Li et al1 wrote (page 1262, first column): ââŚthe result will be a mixture [of the patterns in Table 1]⌠The changes in the pair of regression coefficients from comparing Model 3 with Models 1 and 2 will apply, allowing assessment of evidence for causality still to be madeâ. To illustrate, Li et al1 provided two real data examples. In one of their examples, the exposure was body mass index (BMI) measured at baseline, and the outcome was BMI measured at a later time point during follow-up. Data were collected on adult twins from 250 monozygotic twin pairs. From the temporal order of the BMI measures, we can rule out reverse causation a priori. However, there is clearly a high potential for both confounding (familial as well as within-individual) and causation. In particular, the members of an adult twin pair may have very different eating and exercise habits from each other, which could then be strong unmeasured within-individual confounders for BMI measures over time. Li et al1 presented the following estimated regression coefficients: βself=0.81â , βco-twin=0.73â , βselfâ˛=0.73 and βco-twinâ˛=0.15â . The pattern of these coefficients is a mixture of âFamilial confoundingâ and âX causes Yâ in Table 1, with the attenuation from βco-twin to βco-twinⲠbeing stronger than the attenuation from βself to βselfâ˛â . Li et al1 concluded that these results are â⌠consistent with a longitudinal causation, as well as a small amount of familial confoundingâ. We do not disagree with this conclusion, which sounds intuitively appealing given the nature of BMI and its stability over time, even before doing any study on the topic. However, since the pattern of regression coefficients in Table 1 are derived under the unrealistic assumption of no unmeasured within-individual confounding, we fail to see that the presented regression coefficients give any strong further support for this hypothesis. If we are open to the presence of unmeasured within-individual confounding, the results would also be consistent with other possible mechanisms, such as a large amount of familial confounding together with a small amount of causation, or even a total absence of causation. We demonstrate this with numerical examples in the Supplementary material where the mechanisms in Figure 1a-c all give virtually the same coefficients as above for the BMI data. In the presence of unmeasured within-individual confounding, the regression coefficients alone simply cannot discriminate between these three mechanisms. This can also be seen directly from the causal diagrams. Consider the causal diagram in Figure 1a, where causation is entirely absent. In this diagram, Xself and Yself are associated through two paths: XselfâSXYâYself and XselfâUselfâYselfâ , whereas Xco-twin and Yself are only associated though the first path, which could explain why βself> βco-twinâ . When conditioning on Xco-twinâ , the path XselfâSXâXco-twinâSXYâYself becomes open, which could explain why βself>βâ˛selfâ . Similarly, when conditioning on Xselfâ , the path Xco-twinâSXâXselfâUself âYself becomes open, which could explain why βco-twin>βâ˛co-twinâ . In this note, we have demonstrated some inaccuracies in the derivation of the ICE FALCON method, and highlighted that the method fails to distinguish between competing causal hypotheses in the presence of within-individual confounding. Even in their title, Li et al1 proposed that ICE FALCON was âanalogousâ to MR, and further claimed in their key messages that a benefit over MR would be that ICE FALCON âdoes not make strong assumptionsâ. We think the comparison to MR is overstated and misleading, as the ICE FALCON cannot be described as an instrumental variable method, uses completely different types of data, and does not lend itself to an estimation of the causal effect even when the (indeed) very strong assumptions underlying it are fulfilled. Whereas we have focused on the most important problems with the paper by Li et al,1 there are other, more technical issues with the paper as well, which we discuss in the Supplementary material. In brief, their mathematical derivations have an error that potentially invalidates their results, even in the absence of unmeasured within-individual confounding, and they used GEEs in an inappropriate way that is almost guaranteed to give bias for twin data. The latter issue does not invalidate the ICE FALCON method per se, but it does potentially invalidate their real data analysis results. Yet another issue worth mentioning is the extension of the ICE FALCON method to non-linear models. Li et al1 appear to claim that this extension is trivial, by stating (page 1266) that âICE FALCON is based on regression, so the method can be applied to continuous and binary outcomes using ordinary and logistic regression, respectively, and potentially to survival data using Cox regression. There are no restrictions on the measurement scale of exposuresâ. This seems overly optimistic, given that their Supplementary material proofs use analytic results for linear regression coefficients that are not easily transferred to non-linear models. In particular, due to the non-collapsibility of odds ratios and hazard ratios,5 we conjecture that it is very hard to derive universal patterns of the regression coefficients of logistic regression models and Cox regression models under the mechanisms in Figure 1, even in the absence of unmeasured within-individual confounders. The idea that underlying mechanisms can be inferred for family data by comparing (changes in) regression coefficients is not new. Hudson et al6 also considered the causal diagrams in Figure 1, and discussed what can be inferred about familial confounding from Models 1â3. However, they were substantially more modest in their conclusions than Li et al.1 They concluded that familial confounding can be ruled in by a non-zero coefficient βco-twinâ , provided that one a priori rules out both causation and reverse causation. This fact follows immediately by noting that, in Figure 1a, the only explanation for an association between Xco-twin and Yself (e.g. non-zero βco-twinâ ) is the presence of familial confounders SXYâ . They also carried out a simulation, which indicated that the degree of familial confounding may often lie between βco-twin and βâ˛co-twinâ , when causation is present. However, they cautioned the reader that a simulation does not provide definitive evidence, and unlike Li et al, acknowledged that their particular simulation made several strong assumptions (e.g. normally distributed errors, no statistical interactions, all effects being positive, etc) that will not hold in all real studies. We have repeatedly argued that the complete absence of unmeasured within-individual confounding is very unlikely in practice, but some might counter that the absence of unaccounted for confounding is necessary to draw causal conclusions from all observational studies, and thus that this is not a unique weakness of the ICE FALCON method. To this we would reply that there is a large difference between the common practice in epidemiology where we remain open to the idea that the reported association remains partly confounded (discussing the risk and magnitude of residual confounding, often in relation to differently adjusted models), and the ICE FALCON where we on the one hand must assume that there is confounding by some factors shared identically by relatives (else the method is meaningless), and on the other hand assume that there is no confounding by anything which is correlated less than 1 between twins. Since most potential confounders are somewhere in between (genetic markers would, e.g. be correlated 0.5 in first degree relatives), we can only imagine this to be a plausible assumption when we already have so much knowledge about the research question that it is no longer meaningful to rule out alternative hypotheses for the causation. In particular, if we are interested in estimating a causal effect when we suspect there may be familial confounding but no other bias, we should use a standard sibling comparison design,7 which requires fewer models and gives us a direct estimate of the effect size. We also note that, if the ICE FALCON method is used for other types of relatives than twins (e.g. ordinary siblings or half-siblings), then one would expect the sets of within-individual confounders to be larger for less related individuals. Finally, we note that the ICE FALCON method can only, at best, indicate which underlying mechanisms are at play, but does not provide estimates of their relative importance. Such estimates can be obtained with variance decomposition through structural equation modelling; see Maes et al8 and the references therein. Since there are no new data associated with this article, there was no need for ethics approval. There are no new data associated with this article. Supplementary data are available at IJE online. All work for this paper was carried out by Arvid SjĂślander and Thomas Frisell jointly. This work was supported by the Swedish Research Council [2020-01188 to A.S.]. None declared. Artificial intelligence (AI) was not used for any parts of this paper.
The urgent call to decarbonize our energy infrastructure, while simultaneously meeting growing energy demands, highlights the need for reliable and clean energy sources. Nuclear energy provides reliable, high-capacity baseload electricity while emitting zero greenhouse gases during operation. To adequately meet the energy needs of society and maintain economic viability, it is crucial to enhance the efficiency of nuclear power plant (NPP) operations. Upgrades to NPP operations require near-term Advanced technology Fuel (ATF), such as doped UO 2 , to increase the flexibility of plant operation without impacting safety margins. Small additions of metal oxide dopants are reported to increase grain size, thereby limiting fission gas release (FGR) and increasing pellet compliance to mitigate pellet-chemical interactions (PCI) and pellet-cladding mechanical interactions (PCMI). Prior to implementing doped UO 2 fuels into the reactor fleet, it is important to understand dopant effects on fracture behavior as it impacts fuel performance, such as thermal conductivity, and its tolerance to accident conditions. The availability of fracture data for irradiated and unirradiated UO 2 is limited, while only one study (N = 7, where N is the number of test samples) is available for unirradiated doped UO 2 . Hence, a knowledge-gap exists in the literature for fracture behavior of doped UO 2 fuel forms. The existing knowledge-gap in fuel fracture analysis partly stems from the inherent challenges in machining radiological materials into samples suitable for the traditional bend bar tests. Consequently, acquiring sufficient data to understand the stochastic fracture behavior of ceramic materials is difficult. The ball-on-ring (BOR) biaxial flexure test method utilizes simple right cylindrical geometries representative of commercial nuclear fuel, requires minimal surface preparation, and is tolerant of edge defects; these advantages reduce the time and cost of sample production. As a full understanding of the statistical fracture behavior for ATF concepts has not been established, this work aims to develop and establish the BOR test method to obtain statistical fracture data of undoped and doped UO 2 , providing insight into fracture behavior. Chapter two of this work presents a study performed to validate the BOR biaxial flexure technique using technical ceramics with well-known mechanical properties complemented with finite element analysis (FEA). Chapter three details a test case of CeO 2 and Ti-doped CeO 2 to obtain statistical fracture data. The CeO 2 material was selected as a surrogate for UO 2 to refine sample processing, characterization techniques, and the BOR test method for undoped and doped UO 2 . The research study performed on CeO 2 and Ti-doped CeO 2 was motivated by its use as an electrolyte material for intermediate temperature solid oxide fuel cells (IT-SOFCs). The Ti-CeO 2 samples were doped with 0.1 weight percent (wt%) TiO 2 and resulted in an increased characteristic strength (â 20%) and Weibull modulus compared to CeO 2 , making them a more robust option for IT-SOFCs. In the context of this collective study, it was intended to provide proof of concept for the BOR test method for the testing of UO 2 . Chapter four details the work to produce a benchmark dataset to establish the fracture behavior of undoped UO 2 using the BOR method. This work provides a robust dataset for a comparative analysis of the fracture behavior of doped UO 2 and future fracture studies of ATF concepts. Hertzian contact damage was observed for undoped UO 2 test batch 1 due to the small diameter loading ball (â 3 mm), which was no longer observed in test batch 2 with a larger loading ball (â 19 mm). The contact damage did not appear to influence fracture behavior as both datasets resulted in a characteristic strength and Weibull modulus that agrees with previously published transverse rupture strength (TRS) values for undoped UO 2 . In chapter five, the statistical fracture of doped UO 2 was acquired for UO 2 doped with TiO 2 or Cr 2 O 3 to investigate the effects of dopants on the fracture behavior of UO 2 . The interplay among grain size, dopant-induced defect structures, and pore size and distribution were explored. Both TiO 2 and Cr 2 O 3 doped UO 2 sample sets resulted in lattice contraction and a characteristic strength and Weibull modulus that were lower than expected based on density, pore size, and distribution. The increased grain size of TiO 2 doped UO 2 samples was expected to reduce the fracture strength, yet residual tensile stresses attributed to dopant incorporation in the UO 2 lattice had a greater impact on fracture behavior. Doped UO 2 samples resulted in a reduced fracture strength and with a larger scatter in TRS values. Collectively, the body of this work establishes a BOR test method for the rapid fabrication and mechanical testing of UO 2 and ATF concepts and presented a comparative analysis of fracture behavior for undoped and doped UO 2 fuels. The statistical fracture data presented in this study provide baseline data for enhanced fuel performance code predictions of fuel fracture behavior impacting phenomena during reactor operation. This work provides foundational analysis of fracture behavior to advance research on ATF concepts and assist in acceleration of fuel qualification for the current and future nuclear reactor fleets.
Warhead verification systems proposed to date fundamentally rely on the use of information barriers to prevent the release of sensitive information. Measurements with information barriers significantly increase the complexity of inspection systems, make their certification and authentication difficult, and may reduce the overall confidence in the verifiability of future arms-control agreements. This article presents a concept for a new approach to nuclear warhead verification that minimizes the role of information barriers from the outset and envisions instead an inspection system that avoids the measurement of sensitive information, using a so-called zero-knowledge protocol. This is a protocol in which the data learned by one party (i.e., the inspector) allow him/her to verify that a statement is true (e.g., the inspected warhead is identical to an authenticated template), but does not reveal any additional information, e.g., does not leak any information that would help infer the design of the inspected warhead. There is a wide literature on zero knowledge proofs in the digital domain using cryptographic tools, and we draw on these ideas to achieve this in the physical domain. The proposed inspection system relies on active interrogation of a test object with 14-MeV neutrons, including both tomographic transmission measurements that are sensitive to warhead configuration, and scattering/fission measurements that are sensitive to material properties. The viability of the method is examined with MCNP Monte Carlo neutron transport calculations modeling the experimental setup.