Random Pairs Research Articles

Converter valve-level fault location method based on the temporal differences among horizontal and longitudinal valve states

AC fault or converter fault could lead to LCC-HVDC converter protection operation, and converter protection outlet involves a random bypass pair scheme, which would expand the fault. To address this issue, a converter valve-level fault location method based on temporal differences among horizontal and longitudinal valve states is proposed. The research focuses on the inverter as the object, and analyzes the circuit state characteristics at the different fault locations within converter. In the horizontal direction of converter structure, conduction widths of AC current are constructed based on the location of commutation groups. In the converter longitudinal direction, temporal features of conduction widths are constructed based on single bridge or two bridges. Firstly, fault area is identified based on the amplitude characteristics of converter terminal currents and the abnormal characteristics of valve states. Secondly, converter internal fault is located by using the difference in the horizontal conduction width and the longitudinal temporal features between two bridges. Thirdly, the faulty phase or faulty valve is located as the valve that has the greatest virtual conduction width within the time window interval. Finally, simulations and field record data verify the validity of the proposed fault location method, and show that the proposed method has strong adaptability.

Chronic opioid use and mortality outcomes in patients admitted with COVID-19: A retrospective cohort study.

We hypothesized that chronic opioid users would likely have worse outcomes with COVID-19 infection. A retrospective review of electronic medical records was conducted for all COVID-19 patients admitted in two large academic hospitals in New York City from March 1, 2020 to June 30, 2020 during the onset of the COVID-19 pandemic. A total of 1,361 patients (1,289 opioid naïve patients, 72 with chronic opioid use) were included. A propensity score matched analysis was used to create a dataset. A logistic regression using the generalized estimating equations method was used to evaluate oxygen requirements including bilevel positive airway pressure (BiPAP), high flow nasal cannula (HFNC), and mechanical ventilation (MV). Cox models with random match pairs were fitted for time spent until hospital discharge and in-hospital mortality. The propensity score matched analysis did not demonstrate a significant difference between the chronic opioid use group vs the opioid naïve group for the use of oxygen support (p = 0.439), BiPAP (p = 0.377), HFNC (p = 0.978), or MV (p = 0.080), and length of stay (LOS) (p = 0.950). There was also no statistically significant finding for reduced need for MV (odds ratio 0.42, 95 percent CI: 0.16-1.11, p = 0.080) and lower in-hospital mortality (hazard ratio 0.75, 95 percent CI: 0.39-1.43, p = 0.378) in the chronic opioid use group; however, future larger studies will be needed. Our study did not demonstrate a significant difference in outcomes in patients with COVID-19 with preadmission chronic opioid use vs opioid naïve patients in oxygen requirements, LOS, MV, or mortality. Future studies are needed to further illustrate the impact of opioids on COVID-19 outcomes.

Inverse distance weighting to rapidly generate large simulation datasets

Obtaining large biomechanical datasets for machine learning is an ongoing challenge. Physics-based simulations offer one approach for generating large datasets, but many simulation methods, such as computed muscle control (CMC), are computationally costly. In contrast, interpolation methods, such as inverse distance weighting (IDW), are computationally fast. We examined whether IDW is a low-cost and accurate approach for interpolating muscle activations from CMC.IDW was evaluated using lateral pinch simulations in OpenSim. Simulated pinch data were organized into grids of varying sparsity (high, medium, and low density), where each grid point represented the muscle activations associated with a unique combination of mass and height of a young adult. For each grid, muscle activations were calculated via CMC and IDW for 108 random mass-height pairs that were not coincident with simulation grid vertices. We evaluated the interpolation errors from IDW for each grid, as well as the sensitivity of lateral pinch force to these errors. The root mean square error (RMSE) associated with interpolated muscle activations decreased with increasing grid density and never exceeded 4%. While CMC received a target thumb-tip force of 40 N, errors from the interpolated muscle activations never impacted the simulated force magnitude by more than 0.1 N. Furthermore, the computation time for CMC simulations averaged 4.22 core-minutes, while IDW averaged 0.95 core-seconds per mass-height pair.These results indicate IDW is a practical approach for rapidly estimating muscle activations from sparse CMC datasets. Future works could adapt our IDW approach to evaluate other tasks, biomechanical features, and/or populations.

Rank intraclass correlation for clustered data.

Clustered data are common in biomedical research. Observations in the same cluster are often more similar to each other than to observations from other clusters. The intraclass correlation coefficient (ICC), first introduced by R. A. Fisher, is frequently used to measure this degree of similarity. However, the ICC is sensitive to extreme values and skewed distributions, and depends on the scale of the data. It is also not applicable to ordered categorical data. We define the rank ICC as a natural extension of Fisher's ICC to the rank scale, and describe its corresponding population parameter. The rank ICC is simply interpreted as the rank correlation between a random pair of observations from the same cluster. We also extend the definition when the underlying distribution has more than two hierarchies. We describe estimation and inference procedures, show the asymptotic properties of our estimator, conduct simulations to evaluate its performance, and illustrate our method in three real data examples with skewed data, count data, and three-level ordered categorical data.

BERTrand-peptide:TCR binding prediction using Bidirectional Encoder Representations from Transformers augmented with random TCR pairing.

The advent of T-cell receptor (TCR) sequencing experiments allowed for a significant increase in the amount of peptide:TCR binding data available and a number of machine-learning models appeared in recent years. High-quality prediction models for a fixed epitope sequence are feasible, provided enough known binding TCR sequences are available. However, their performance drops significantly for previously unseen peptides. We prepare the dataset of known peptide:TCR binders and augment it with negative decoys created using healthy donors' T-cell repertoires. We employ deep learning methods commonly applied in Natural Language Processing to train part a peptide:TCR binding model with a degree of cross-peptide generalization (0.69 AUROC). We demonstrate that BERTrand outperforms the published methods when evaluated on peptide sequences not used during model training. The datasets and the code for model training are available at https://github.com/SFGLab/bertrand.

A novel training point selection strategy guided by the maximum reduction of structural state misclassification probability for time-dependent reliability analysis

When adaptively selecting training point in Kriging model based time-dependent reliability analysis, existing methods may lose efficiency due to less considering the Kriging prediction correlation at different time instant as well as the interaction of random input and time variable. Thus, a novel training point selection strategy is proposed by maximizing structural state misclassification probability (SSMP) reduction. Firstly, by taking the Kriging prediction correlation at different time instant into account, the SSMP is derived for random input candidate sample. Secondly, since it is inefficient to actually evaluate SSMP, the expected SSMP is approximately derived with the current Kriging model information by virtually adding the random input and time candidate sample pair into training set. Then, the SSMP reduction, i.e., the difference between the SSMP derived in first step and the expected SSMP in the second one, can be evaluated. By actually adding the random input and time candidate sample pair with the maximum SSMP reduction into training set, the novel training point selection strategy is proposed to update the Kriging model for minimizing SSMP expectedly. Due to considering the Kriging prediction correlation in deriving SSMP, as well as the interaction of random input and time in evaluation the SSMP reduction, the maximum SSMP reduction guided training point selection strategy is superior to the up-to-date methods. The presented example results show that the proposed method needs a least number of evaluating performance function in four compared adaptive Kriging model based methods, and the reduction number of evaluating performance function of the proposed method with respect to the up-to-date methods is more in complex engineering examples than in the simple numerical ones.

Interpolating Graph Pair to Regularize Graph Classification

We present a simple and yet effective interpolation-based regularization technique, aiming to improve the generalization of Graph Neural Networks (GNNs) on supervised graph classification. We leverage Mixup, an effective regularizer for vision, where random sample pairs and their labels are interpolated to create synthetic images for training. Unlike images with grid-like coordinates, graphs have arbitrary structure and topology, which can be very sensitive to any modification that alters the graph's semantic meanings. This posts two unanswered questions for Mixup-like regularization schemes: Can we directly mix up a pair of graph inputs? If so, how well does such mixing strategy regularize the learning of GNNs? To answer these two questions, we propose ifMixup, which first adds dummy nodes to make two graphs have the same input size and then simultaneously performs linear interpolation between the aligned node feature vectors and the aligned edge representations of the two graphs. We empirically show that such simple mixing schema can effectively regularize the classification learning, resulting in superior predictive accuracy to popular graph augmentation and GNN methods.

Adversarial MixUp with implicit semantic preservation for semi-supervised hyperspectral image classification

MixUp generates virtual samples by performing the identical convex combination in feature and semantic spaces simultaneously. However, convexly combining random pairs of images and their associated labels is likely to result in misunderstandings between the generated sample and its assigned pseudo label, particularly for hyperspectral images (HSI), leading to a confusing effect on the classifier. In this paper, adversarial MixUp with implicit semantic preservation (AdvMixup) is proposed for semi-supervised HSI classification (HSIc). The proposed AdvMixup exploits interpolation in the latent space for unlabeled samples. The virtual hyperspectral sample is generated by a deconvolutional network on the interpolated latent data. A semantic preservation network is performed on the newly generated virtual sample to recover the MixUp coefficient, where the semantic is preserved implicitly in the virtual sample. Meanwhile, an adversarial regularization is also conducted on the recovered mixup coefficient to ensure the authenticity of the virtual HSI. In such a way, the proposed AdvMixup sees the unseen HSI and knows the unknown semantic. Throughout the learning process, the feature extraction network is shared in both supervised and unsupervised branches to obtain a superior decision boundary. Experimental results on three HSI benchmark datasets demonstrate that AdvMixup achieves state-of-the-art performance in semi-supervised HSI classification.

Copula‐based importance sampling method for efficient slope reliability analysis

AbstractEfficient slope reliability analysis that accounts for the interdependencies of random variables is challenging. In this study, an efficient reliability method is proposed based on importance sampling (IS) and copulas. First, the IS method based on the design point is introduced to construct the marginal IS density. Copulas are subsequently adopted to capture the interdependencies and establish both the initial joint distributions and the joint IS densities of random variable pairs. The IS algorithm is modified to consider the dependencies through not only the estimation of the probability distribution but also random sampling. Finally, a framework of the copula‐based IS method is constructed. The applicability, accuracy, efficiency, and robustness of the proposed method were validated by a classical slope case. The results showed that with the proposed method, slope reliability could be efficiently assessed with a relatively high accuracy. The dependencies of the variables significantly affected the IS and final slope reliability, whereas the IS density had a significantly lower effect. The proposed method combines the advantages of IS and copulas well. Interdependencies of the variables can be properly characterized during sampling. Moreover, the proposed method was shown to be robust regardless of the system failure probability level. It can be further applied to improve the random finite element method in the future.

Interobserver Agreement on Intracranial Hemorrhage on Magnetic Resonance Imaging in Patients With Ischemic Stroke.

The Heidelberg Bleeding Classification, developed for computed tomography, is also frequently used to classify intracranial hemorrhage (ICH) on magnetic resonance imaging. Additionally, the presence of any ICH is frequently used as (safety) outcome measure in clinical stroke trials that evaluate acute interventions. We assessed the interobserver agreement on the presence of any ICH and the type of ICH according to the Heidelberg Bleeding Classification on magnetic resonance imaging in patients treated with reperfusion therapy. We used 300 magnetic resonance imaging scans including susceptibility-weighted imaging or T2*-weighted gradient echo imaging of ischemic stroke patients within 1 week after reperfusion therapy. Six observers, blinded to clinical characteristics except for suspected location of the infarction, independently rated ICH according to the Heidelberg Bleeding Classification in random pairs. Percent agreement and Cohen's kappa (κ) were estimated for the presence of any ICH (yes/no), and for agreement on the Heidelberg Bleeding Classification class 1 and 2. For the Heidelberg Bleeding Classification class 1 and 2, weighted κ was estimated to take the degree of disagreement into account. In 297 of 300 scans, the quality of scans was sufficient to score ICH. Observers agreed on the presence or absence of any ICH in 264 of 297 scans (88.9%; κ 0.78 [95% CI, 0.71-0.85]). There was agreement on the Heidelberg Bleeding Classification class 1 and 2 and no ICH in class 1 and 2 in 226 of 297 scans (76.1%; κ 0.63 [95% CI, 0.56-0.69]; weighted κ 0.90 [95% CI, 0.87-0.93]). The presence of any ICH can be reliably scored on magnetic resonance imaging and can, therefore, be used as (safety) outcome measure in clinical stroke trials that evaluate acute interventions. Agreement of ICH types according to the Heidelberg Bleeding Classification is substantial and disagreements are small.

Enhancing Knowledge Management in Healthcare: An Embedding Fusion Approach to Business Rule Representation

Enterprise Decision Management systems are vital for delivering efficient healthcare services. However, the ever-changing clinical terminology creates complex business rules, making healthcare IT systems difficult to maintain. In this study, we present an embedding fusion technique using unsupervised Natural Language Processing (NLP) to represent business rules as semantic vectors by incorporating multiple text data sources for each rule. We apply this method to a dental insurance administration case study and find that our approach is over 200 times more likely to identify redundant rule pairs compared to random pairs. This case study suggests that an embedding-based technique can significantly improve knowledge management efficiency in healthcare IT systems.

Management of diversity and inbreeding when importing new stock into an inbred population.

This article relates to breeding programs that seek to manage genetic diversity. The method maximizes a multicomponent objective function, applicable across breeding scenarios. However, this paper focuses on breeding decisions following immigration of 10 unrelated individuals into a highly inbred simulated population (F ≈ 0.34). We use Optimal Contribution Selection to maximize retention of genetic diversity. However, some treatments add Coancestry Assortative Mating (CAM). This helps to avoid early dilution of immigrant genetic material, maximizing its ability to contribute to genetic diversity in the longer term. After 20 generations, this resulted in considerably increased genetic diversity, with mean coancestries 59% of what random pairing gave. To manage progeny inbreeding, common practice is to reject matings above an upper limit. As a suboptimal rules-based approach, this resulted in 26% decreased genetic diversity and 8% increased inbreeding in the long term, compared with random pairing. In contrast, including mean progeny inbreeding as a continuous variable in the overall objective function decreased final inbreeding by 37% compared with random pairing. Adding some emphasis on selection for a single trait resulted in a similar pattern of effects on coancestry and inbreeding, with 12% higher trait response under CAM. Results indicate the properties of alternative methods, but we encourage users to do their own investigations of particular scenarios, such as including inbreeding depression. Practical implementation of these methods is discussed: they have been widely adopted in domestic animal breeding and are highly flexible to accommodate a wide range of technical and logistical objectives and constraints.

Ultra-efficient generation of time-energy entangled photon pairs in an InGaP photonic crystal cavity

The typical approaches to generate heralded single photons rely on parametric processes, with the advantage of generating highly entangled states at the price of a random pair emission. To overcome this limit, degenerate spontaneous Four-Wave-Mixing is a reliable technique which combines two pump photons into a pair of signal and idler photons via Kerr nonlinear optical effect. By exploiting the intrinsic small confinement volume and thermally tuning the resonances of a 20 μm-long Photonic Crystal cavity, we efficiently generate time-energy entangled photon pairs and heralded single photons at a large maximum on-chip rate of 22 MHz, using 36 μW of pump power. We measure time-energy entanglement with net visibility up to 96.6 % using 1 second integration time constant. Our measurements demonstrate the viability of Photonic Crystal cavities to act as an alternative and efficient photon pair source for quantum photonics.

Assortative preferences for personality and online dating apps: Individuals prefer profiles similar to themselves on agreeableness, openness, and extraversion

IntroductionEstablished couples tend to have similar personalities (i.e., assortative mating); however, the mechanism for this effect is unclear. Individuals may initially be attracted to others who are like themselves (i.e., have assortative preferences). Alternatively, couples may become more similar over time. These explanations have been difficult to disentangle. Assortative mating may be less common in online situations as barriers related to social homogamy are removed. The current study experimentally investigates which, if any, of the Big Five personality traits were assortatively preferred in an online environment. MethodsOnline volunteers and paid participants (205 females and 178 males) viewed 100 ostensible dating profiles comprised of random pairings of facial images and personal descriptions, the latter of which were pre-rated for perceived personality. Participants indicated whether they would like to “match” with each profile, mimicking responses made on dating applications, and completed the Big Five Inventory (BFI-44). ResultsParticipants showed assortative preferences for agreeableness, openness, and extraversion, but not for conscientiousness or emotional stability. ConclusionThese results suggest that people exhibit assortative preferences in an online dating app environment. If these online preferences translate to long-term relationships, this could help explain similarities found in established couples identified in previous research.

Optimal User Pairing Approach for NOMA-Based Cell-Free Massive MIMO Systems

This study investigates a non-orthogonal multiple access (NOMA)-assisted cell-free massive multiple-input multiple-output (MIMO) system, considering the impact of both individual and linear-combination channel estimations. To make the best use of NOMA as an enabler for cell-free massive MIMO systems, user pairing should be employed effectively. Random user pairing naturally leads to a non-optimal solution, whereas an exhaustive search approach is unfavorable for practical systems owing to the high complexity. In this study, we propose an optimal user pairing strategy to group users that jointly optimize the minimum downlink rate per user and power allocation at an acceptable cost of complexity. To address this problem, we first relax the binary variables to continuous variables and then develop an iterative algorithm based on the inner approximation method, yielding at least one locally optimal solution. Numerical results show that the proposed user pairing algorithm outperforms existing counterparts, such as conventional beamforming, random pairing, far pairing, and close-pairing strategies, while it can be performed dynamically, that is, two arbitrary users satisfying the formulated problem can be paired regardless of geographical distance. Finally, our approach demonstrates that the combination channel estimation-based NOMA-assisted cell-free massive MIMO achieves the best result in terms of the downlink rate per user when associated with the proposed algorithm.

Physiological and Functional Effects of Dominant Active TCRα Expression in Transgenic Mice

A T cell receptor (TCR) consists of α- and β-chains. Accumulating evidence suggests that some TCRs possess chain centricity, i.e., either of the hemi-chains can dominate in antigen recognition and dictate the TCR's specificity. The introduction of TCRα/β into naive lymphocytes generates antigen-specific T cells that are ready to perform their functions. Transgenesis of the dominant active TCRα creates transgenic animals with improved anti-tumor immune control, and adoptive immunotherapy with TCRα-transduced T cells provides resistance to infections. However, the potential detrimental effects of the dominant hemi-chain TCR's expression in transgenic animals have not been well investigated. Here, we analyzed, in detail, the functional status of the immune system of recently generated 1D1a transgenic mice expressing the dominant active TCRα specific to the H2-Kb molecule. In their age dynamics, neither autoimmunity due to the random pairing of transgenic TCRα with endogenous TCRβ variants nor significant disturbances in systemic homeostasis were detected in these mice. Although the specific immune response was considerably enhanced in 1D1a mice, responses to third-party alloantigens were not compromised, indicating that the expression of dominant active TCRα did not limit immune reactivity in transgenic mice. Our data suggest that TCRα transgene expression could delay thymic involution and maintain TCRβ repertoire diversity in old transgenic mice. The detected changes in the systemic homeostasis in 1D1a transgenic mice, which are minor and primarily transient, may indicate variations in the ontogeny of wild-type and transgenic mouse lines.

Lensing or luck? False alarm probabilities for gravitational lensing of gravitational waves

Strong gravitational lensing of gravitational waves (GWs) has been forecasted to become detectable in the upcoming LIGO/Virgo/KAGRA observing runs. However, definitively distinguishing pairs of lensed sources from random associations is a challenging problem. We investigate the degree to which unlensed events mimic lensed ones because of the overlap of parameters due to a combination of random coincidence and errors in parameter estimation. Lensed events are expected to have consistent masses and sky locations, and constrained relative phases, but may have differing apparent distances due to lensing magnification. We construct a mock catalog of lensed and unlensed events. We find that the probability of a false alarm based on coincidental overlaps of the chirp mass, sky location, and coalescence phase are approximately 9%, 1%, and 10% per pair, respectively. Combining all three parameters, we arrive at an overall false alarm probability per pair of $\ensuremath{\sim}{10}^{\ensuremath{-}4}$. We validate our results against the GWTC-2 data, finding that the catalog data is consistent with our simulations. As the number of events, $N$, in the GW catalogs increases, the number of random pairs of events increases as $\ensuremath{\sim}{N}^{2}$. Meanwhile, the number of lensed events will increase linearly with $N$, implying that, for sufficiently high $N$, the false alarms will always dominate over the true lensing events. This issue can be compensated for by placing higher thresholds on the lensing candidates (e.g., selecting a higher signal-to-noise ratio (SNR) threshold, ${\ensuremath{\rho}}_{\mathrm{thr}}$), which will lead to better parameter estimation and, thus, lower false alarm probabilities per pair---at the cost of dramatically decreasing the size of the lensing sample ($\ensuremath{\propto}{\ensuremath{\rho}}_{\mathrm{thr}}^{\ensuremath{-}3}$). We show that with our simple overlap criteria for current detectors at design sensitivity, the false alarms will dominate for realistic lensing rates ($\ensuremath{\lesssim}{10}^{\ensuremath{-}3}$) even when selecting the highest SNR pairs. These results highlight the necessity to design alternative identification criteria beyond simple waveform and sky location overlap for conclusive detection of strong lensing. Future GW detectors such as Cosmic Explorer and Einstein Telescope may provide sufficient improvement in parameter estimation and a commensurate decrease in the incidence of coincidental overlap of parameters, allowing for the conclusive detection of strong lensing of GWs even without additional detection criteria.

Investigating the Effects of Storytelling Method on Students’ Memory at Primary Level in (KPK)

Methodology bears very concrete role-in the-teaching learning-processto convey any learning material, psychologists and educationists haverecommended both cognitive and behavioral methods in this regard.Storytelling method is one of these methods being applied in theclassroom teaching. Storytelling involves two-way encounters betweena storyteller and one or more listeners. The answers of the listeners affectthe plot. In reality, storytelling arises from the engagement and mutual,organized efforts of the storyteller and the audience. This study wasaimed at investigating the method of increasing the memory of studentsof class 4th in the subject of English. Objectives of the study were: (i) toanalyze the effectiveness of storytelling method of teaching, (ii) to findout the impact of storytelling method on the memory increase ofstudents, (iii) to explore the motivational effects of storytelling methodon students, (iv) to investigate the effects of storytelling method onreading fluency of students. The study population was all girls inNowshera district primary schools. As a sample of the report, 40 grade 4students from a Government Girls Primary School were taken. Thesestudents were divided into two classes, which were experimental andcontrolled by random pair sampling on the basis of pre-test and post-test.Pre-test and post-test were used as analysis tools; the data obtained wastabulated and analyzed using t-test and percentage in the light of thestudy objectives. The analysis of the collected data revealed thefollowing findings. It was concluded from the results that Storytellingmethod had significant effect on students’ achievement and the learnertook interest in the learning. The result of the study showed thatstorytelling method had significant impact on memory increase ofstudents. Hence it is recommended that teachers may teach elementarysubjects through storytelling methods and Government should arrangeteacher’s refresher course for storytelling method. It is recommended that teachers should adopt the storytelling method while teaching atelementary level. It was concluded that storytelling method hadsignificance motivational effect on students.

The Arctan Power Distribution: Properties, Quantile and Modal Regressions with Applications to Biomedical Data

The usefulness of (probability) distributions in the field of biomedical science cannot be underestimated. Hence, several distributions have been used in this field to perform statistical analyses and make inferences. In this study, we develop the arctan power (AP) distribution and illustrate its application using biomedical data. The distribution is flexible in the sense that its probability density function exhibits characteristics such as left-skewedness, right-skewedness, and J and reversed-J shapes. The characteristic of the corresponding hazard rate function also suggests that the distribution is capable of modeling data with monotonic and non-monotonic failure rates. A bivariate extension of the AP distribution is also created to model the interdependence of two random variables or pairs of data. The application reveals that the AP distribution provides a better fit to the biomedical data than other existing distributions. The parameters of the distribution can also be fairly accurately estimated using a Bayesian approach, which is also elaborated. To end the study, the quantile and modal regression models based on the AP distribution provided better fits to the biomedical data than other existing regression models.

Coordinated evolution at amino acid sites of SARS-CoV-2 spike.

SARS-CoV-2 has adapted in a stepwise manner, with multiple beneficial mutations accumulating in a rapid succession at origins of VOCs, and the reasons for this are unclear. Here, we searched for coordinated evolution of amino acid sites in the spike protein of SARS-CoV-2. Specifically, we searched for concordantly evolving site pairs (CSPs) for which changes at one site were rapidly followed by changes at the other site in the same lineage. We detected 46 sites which formed 45 CSP. Sites in CSP were closer to each other in the protein structure than random pairs, indicating that concordant evolution has a functional basis. Notably, site pairs carrying lineage defining mutations of the four VOCs that circulated before May 2021 are enriched in CSPs. For the Alpha VOC, the enrichment is detected even if Alpha sequences are removed from analysis, indicating that VOC origin could have been facilitated by positive epistasis. Additionally, we detected nine discordantly evolving pairs of sites where mutations at one site unexpectedly rarely occurred on the background of a specific allele at another site, for example on the background of wild-type D at site 614 (four pairs) or derived Y at site 501 (three pairs). Our findings hint that positive epistasis between accumulating mutations could have delayed the assembly of advantageous combinations of mutations comprising at least some of the VOCs.