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We present results on the isoscalar form factors including the disconnected contributions, as well as on the strange and charm quark form factors. Using previous results on the isovector form factors, we determine the flavor decomposition of the nucleon axial form factors. These are computed using an ensemble of $N_f=2+1+1$ twisted mass fermions simulated with physical values of quark masses. We investigate the SU(3) flavor symmetry and show that there is up to 10\% breaking for the axial and up to 50\% for the induced pseudoscalar form factors. By fitting the $Q^2$-dependence, we determined the corresponding root mean square radii. The pseudoscalar coupling of the $\eta$ meson and the nucleon is found to be $g_{\eta NN}=3.7(1.0)(0.7)$, and the Goldberger-Treiman discrepancy for the octet combination about 50\%.

In this work, we perform a lattice QCD study of the intrinsic, rapidity-independent soft function within the framework of large momentum effective theory. The computation is carried out using a gauge ensemble of $N_f=2+1+1$ clover-improved twisted mass fermion. After applying an appropriate renormalization procedure and the removal of significant higher-twist contamination, we obtain the intrinsic soft function that is comparable to the one-loop perturbative result at large external momentum. The determination of the nonperturbative soft function from first principles is crucial to sharpen our understanding of the processes with small transverse momentum such as the Drell-Yan production and the semi-inclusive deep inelastic scattering. Additionally, we calculate the Collins-Soper evolution kernel using the quasi-transverse-momentum-dependent wave function as input., Comment: 7 pages, 4 figures

We present a ground-based optical transmission spectrum for the warm Saturn-mass exoplanet WASP-110b from two transit observations made with the FOcal Reducer and Spectrograph (FORS2) on the Very Large Telescope (VLT). The spectrum covers the wavelength range from 4000 to 8333\AA, which is binned in 46 transit depths measured to an averaged precision of 220 parts per million (ppm) over an averaged 80\AA~bin for a Vmag=12.8 star. The measured transit depths are unaffected by a dilution from a close A-type field dwarf, which was fully resolved. The overall main characteristic of the transmission spectrum is an increasing radius with wavelength and a lack of the theoretically predicted pressure-broadened sodium and potassium absorption features for a cloud-free atmosphere. We analyze archival high-resolution optical spectroscopy and find evidence for low to moderate activity of the host star, which we take into account in the atmospheric retrieval analysis. Using the AURA retrieval code, we find that the observed transmission spectrum can be best explained by a combination of unocculted stellar faculae and a cloud deck. Transmission spectra of cloud-free and hazy atmospheres are rejected at a high confidence. With a possible cloud deck at its terminator, WASP-110b joins the increasing population of irradiated hot-Jupiter exoplanets with cloudy atmospheres observed in transmission., Comment: Accepted for publication in The Astronomical Journal

We present a calculation of the up, down, strange and charm quark masses performed within the lattice QCD framework. We use the twisted mass fermion action and carry out simulations that include in the sea two light mass-degenerate quarks, as well as the strange and charm quarks. In the analysis we use gauge ensembles simulated at three values of the lattice spacing and with light quarks that correspond to pion masses in the range from 350 MeV to the physical value, while the strange and charm quark masses are tuned approximately to their physical values. We use several quantities to set the scale in order to check for finite lattice spacing effects and in the continuum limit we get compatible results. The quark mass renormalization is carried out non-perturbatively using the RI'-MOM method converted into the $\overline{\rm MS}$ scheme. For the determination of the quark masses we use physical observables from both the meson and the baryon sectors, obtaining $m_{ud} = 3.636(66)(^{+60}_{-57})$~MeV and $m_s = 98.7(2.4)(^{+4.0}_{-3.2})$~MeV in the $\overline{\rm MS}(2\,{\rm GeV})$ scheme and $m_c = 1036(17)(^{+15}_{-8})$~MeV in the $\overline{\rm MS}(3\,{\rm GeV})$ scheme, where the first errors are statistical and the second ones are combinations of systematic errors. For the quark mass ratios we get $m_s / m_{ud} = 27.17(32)(^{+56}_{-38})$ and $m_c / m_s = 11.48(12)(^{+25}_{-19})$., Comment: 37 pages, 23 figures, 24 tables. One reference added

We present a calculation of the pion and kaon Mellin moment $\langle x^3 \rangle$ extracted directly in lattice QCD using a three-derivative local operator. We use one ensemble of gauge configurations with two degenerate light, a strange and a charm quark ($N_f=2+1+1$) of maximally twisted mass fermions with clover improvement. The ensemble reproduces a pion mass $\sim260$ MeV, and a kaon mass $\sim530$ MeV. Excited-states contamination is evaluated using four values of the source-sink time separation within the range of $1.12-1.67$ fm. We use an operator that is free of mixing, and apply a multiplicative renormalization function calculated non-perturbatively. Our results are converted to the $\overline{\rm MS}$ scheme and evolved at a scale of 2 GeV, using three-loop expressions in perturbation theory. The final values are $\langle x^3 \rangle_\pi^{u^+}=0.024(18)_{\rm stat}(2)_{\rm syst}$, $\langle x^3 \rangle_K^{u^+}=0.035(6)_{\rm stat}(3)_{\rm syst}$, and $\langle x^3 \rangle_K^{s^+}=0.075(5)_{\rm stat}(1)_{\rm syst}$, where the systematic error is the uncertainty due to excited state contamination. We combine $\langle x^3 \rangle$ with the two lower moments to obtain the ratios $\langle x^3 \rangle/\langle x \rangle$ and $\langle x^3 \rangle/\langle x^2 \rangle$, as well as ratios between the pion and kaon moments. In addition, we reconstruct the $x$-dependence of the pion and kaon PDFs via 2- and 3-parameter fits to our results. We find that the reconstruction is feasible and that our lattice data favor a large $x$-dependence that falls as $(1-x)^2$ for both the pion and kaon PDFs. We integrate the reconstructed PDFs to extract the higher moments with $4\leq n\leq 6$. Finally, we compare the pion and kaon PDFs, as well as the ratios of their moments, to address the effect of SU(3) flavor symmetry breaking., Comment: 24 pages, 12 figures

The neutron is a cornerstone in our depiction of the visible universe. Despite the neutron zero-net electric charge, the asymmetric distribution of the positively- (up) and negatively-charged (down) quarks, a result of the complex quark-gluon dynamics, lead to a negative value for its squared charge radius, $\langle r_{\rm n}^2 \rangle$. The precise measurement of the neutron's charge radius thus emerges as an essential part of unraveling its structure. Here we report on a $\langle r_{\rm n}^2 \rangle$ measurement, based on the extraction of the neutron electric form factor, $G_{\rm E}^{\rm n}$, at low four-momentum transfer squared $(Q^2)$ by exploiting the long known connection between the $N \rightarrow \Delta$ quadrupole transitions and the neutron electric form factor. Our result, $\langle r_{\rm n}^2 \rangle = -0.110 \pm0.008~({\rm fm}^2)$, addresses long standing unresolved discrepancies in the $\langle r_{\rm n}^2 \rangle$ determination. The dynamics of the strong nuclear force can be viewed through the precise picture of the neutron's constituent distributions that result into the non-zero $\langle r_{\rm n}^2 \rangle$ value., Comment: https://doi.org/10.1038/s41467-021-22028-z

Software projects are regularly updated with new functionality and bug fixes through so-called releases. In recent years, many software projects have been shifting to shorter release cycles and this can affect the bug handling activity. Past research has focused on the impact of switching from traditional to rapid release cycles with respect to bug handling activity, but the effect of the rapid release cycle duration has not yet been studied. We empirically investigate releases of 420 open source projects with rapid release cycles to understand the effect of variable and rapid release cycle durations on bug handling activity. We group the releases of these projects into five categories of release cycle durations. For each project, we investigate how the sequence of releases is related to bug handling activity metrics and we study the effect of the variability of cycle durations on bug fixing. Our results did not reveal any statistically significant difference for the studied bug handling activity metrics in the presence of variable rapid release cycle durations. This suggests that the duration of fast release cycles does not seem to impact bug handling activity., Comment: 8 pages, 6 figures

Development bots are used on Github to automate repetitive activities. Such bots communicate with human actors via issue comments and pull request comments. Identifying such bot comments allows preventing bias in socio-technical studies related to software development. To automate their identification, we propose a classification model based on natural language processing. Starting from a balanced ground-truth dataset of 19,282 PR and issue comments, we encode the comments as vectors using a combination of the bag of words and TF-IDF techniques. We train a range of binary classifiers to predict the type of comment (human or bot) based on this vector representation. A multinomial Naive Bayes classifier provides the best results. Its performance on a test set containing 50% of the data achieves an average precision, recall, and F1 score of 0.88. Although the model shows a promising result on the pull request and issue comments, further work is required to generalize the model on other types of activities, like commit messages and code reviews., Comment: 4 pages, 1 page of reference, 1 figure, 3 tabels

This report describes the physics case, the resulting detector requirements, and the evolving detector concepts for the experimental program at the Electron-Ion Collider (EIC). The EIC will be a powerful new high-luminosity facility in the United States with the capability to collide high-energy electron beams with high-energy proton and ion beams, providing access to those regions in the nucleon and nuclei where their structure is dominated by gluons. Moreover, polarized beams in the EIC will give unprecedented access to the spatial and spin structure of the proton, neutron, and light ions. The studies leading to this document were commissioned and organized by the EIC User Group with the objective of advancing the state and detail of the physics program and developing detector concepts that meet the emerging requirements in preparation for the realization of the EIC. The effort aims to provide the basis for further development of concepts for experimental equipment best suited for the science needs, including the importance of two complementary detectors and interaction regions. This report consists of three volumes. Volume I is an executive summary of our findings and developed concepts. In Volume II we describe studies of a wide range of physics measurements and the emerging requirements on detector acceptance and performance. Volume III discusses general-purpose detector concepts and the underlying technologies to meet the physics requirements. These considerations will form the basis for a world-class experimental program that aims to increase our understanding of the fundamental structure of all visible matter, Comment: 902 pages, 415 authors, 151 institutions

This Letter capitalizes on a unique set of total solar eclipse observations, acquired between 2006 and 2020, in white light, Fe XI 789.2 nm ($\rm T_{fexi}$ = $1.2 \pm 0.1$ MK) and Fe XIV 530.3 nm ($\rm T_{fexiv}$ = $ 1.8 \pm 0.1$ MK) emission, complemented by in situ Fe charge state and proton speed measurements from ACE/SWEPAM-SWICS, to identify the source regions of different solar wind streams. The eclipse observations reveal the ubiquity of open structures, invariably associated with Fe XI emission from $\rm Fe^{10+}$, hence a constant electron temperature, $\rm T_{c}$ = $\rm T_{fexi}$, in the expanding corona. The in situ Fe charge states are found to cluster around $\rm Fe^{10+}$, independently of the 300 to 700 km $\rm s^{-1}$ stream speeds, referred to as the continual solar wind. $\rm Fe^{10+}$ thus yields the fiducial link between the continual solar wind and its $\rm T_{fexi}$ sources at the Sun. While the spatial distribution of Fe XIV emission, from $\rm Fe^{13+}$, associated with streamers, changes throughout the solar cycle, the sporadic appearance of charge states $> \rm Fe^{11+}$, in situ, exhibits no cycle dependence regardless of speed. These latter streams are conjectured to be released from hot coronal plasmas at temperatures $\ge \rm T_{fexiv}$ within the bulge of streamers and from active regions, driven by the dynamic behavior of prominences magnetically linked to them. The discovery of continual streams of slow, intermediate and fast solar wind, characterized by the same $\rm T_{fexi}$ in the expanding corona, places new constraints on the physical processes shaping the solar wind., Comment: 18 pages, 9 figures, accepted for publication in ApJ Letters

English for Specific Purposes (ESP) is an area of language education that has been advancing during the last years due to increased social and professional mobility. Despite this, as shown in the related literature, the area of ESP Teacher Education (TE) is deprived of attention by researchers; as a result, many ESP educators in different countries are General English (GE) teachers with insufficient training in ESP. The present chapter reports on the first findings of a technical action research study, which aims at exploring and addressing the problem of insufficient ESP TE among a specific group of ESP practitioners, suggesting an intervention in the form of an online ESP TE programme. Following the spiral pattern of action research, the study evolves in cycles of continuous improvement. This chapter focusses on the initial stages of the study during which the problem of lack of ESP TE opportunities was identified, and a remedy to this problem, an online ESP TE course, named Online Reflective Teacher Education in ESP (ReTEESP Online), was developed and piloted before its implementation. [For the complete volume, "ESP Teaching and Teacher Education: Current Theories and Practices," see ED595614.]

In an era of continuous technological advancement and severe financial crisis, the cloud computing paradigm has become one of the most prominent and influential developments in information technology since the emergence of the Internet. This chapter describes the second phase of an action research study, which aimed at addressing the problem of lack of appropriate technology tools for the delivery of two blended English for Academic Purposes (EAP) courses for first-year students of the Departments of (1) Agricultural Sciences, Biotechnology, and Food Science and (2) Commerce, Finance, and Shipping, at the Cyprus University of Technology. The solution suggested involved the integration of the G Suite for Education in the teaching and learning process. The suite was firstly introduced in the academic year 2016-2017 (Kakoulli Constantinou, 2018), and the feedback obtained then was valuable for its reintegration the following year. The present chapter focusses on the second attempt to integrate the suite in the context of which data was elicited in order to improve the use of the suite for the delivery of the two EAP courses in the future. [For the complete volume, "Professional Development in CALL: A Selection of Papers," see ED593926.]

Causal Bayesian networks have become a powerful technology for reasoning under uncertainty in areas that require transparency and explainability, by relying on causal assumptions that enable us to simulate hypothetical interventions. The graphical structure of such models can be estimated by structure learning algorithms, domain knowledge, or a combination of both. Various knowledge approaches have been proposed in the literature that enable us to specify prior knowledge that constrains or guides these algorithms. This paper introduces some novel, and also describes some existing, knowledge-based approaches that enable us to combine structure learning with knowledge obtained from heterogeneous sources. We investigate the impact of these approaches on structure learning across different algorithms, case studies and settings that we might encounter in practice. Each approach is assessed in terms of effectiveness and efficiency, including graphical accuracy, model fitting, complexity, and runtime; making this the first paper that provides a comparative evaluation of a wide range of knowledge approaches for structure learning. Because the value of knowledge depends on what data are available, we illustrate the results both with limited and big data. While the overall results show that knowledge becomes less important with big data due to higher learning accuracy rendering knowledge less important, some of the knowledge approaches are found to be more important with big data. Amongst the main conclusions is the observation that reduced search space obtained from knowledge does not always imply reduced computational complexity, perhaps because the relationships implied by the data and knowledge are in tension.

The graph of a Bayesian Network (BN) can be machine learned, determined by causal knowledge, or a combination of both. In disciplines like bioinformatics, applying BN structure learning algorithms can reveal new insights that would otherwise remain unknown. However, these algorithms are less effective when the input data are limited in terms of sample size, which is often the case when working with real data. This paper focuses on purely machine learned and purely knowledge-based BNs and investigates their differences in terms of graphical structure and how well the implied statistical models explain the data. The tests are based on four previous case studies whose BN structure was determined by domain knowledge. Using various metrics, we compare the knowledge-based graphs to the machine learned graphs generated from various algorithms implemented in TETRAD spanning all three classes of learning. The results show that, while the algorithms produce graphs with much higher model selection score, the knowledge-based graphs are more accurate predictors of variables of interest. Maximising score fitting is ineffective in the presence of limited sample size because the fitting becomes increasingly distorted with limited data, guiding algorithms towards graphical patterns that share higher fitting scores and yet deviate considerably from the true graph. This highlights the value of causal knowledge in these cases, as well as the need for more appropriate fitting scores suitable for limited data. Lastly, the experiments also provide new evidence that support the notion that results from simulated data tell us little about actual real-world performance.

The depletion of SO$_2$ and H$_2$O in and above the clouds of Venus (45 -- 65 km) cannot be explained by known gas-phase chemistry and the observed composition of the atmosphere. We apply a full-atmosphere model of Venus to investigate three potential explanations for the SO$_2$ and H$_2$O depletion: (1) varying the below-cloud water vapor (H$_2$O), (2) varying the below-cloud sulfur dioxide (SO$_2$), and (3) the incorporation of chemical reactions inside the sulfuric acid cloud droplets. We find that increasing the below-cloud H$_2$O to explain the SO$_2$ depletion results in a cloud top that is 20 km too high, above-cloud O$_2$ three orders of magnitude greater than observational upper limits and no SO above 80 km. The SO$_2$ depletion can be explained by decreasing the below-cloud SO$_2$ to $20\,{\rm ppm}$. The depletion of SO$_2$ in the clouds can also be explained by the SO$_2$ dissolving into the clouds, if the droplets contain hydroxide salts. These salts buffer the cloud pH. The amount of salts sufficient to explain the SO$_2$ depletion entail a droplet pH of $\sim 1$ at 50 km. Since sulfuric acid is constantly condensing out into the cloud droplets, there must be a continuous and pervasive flux of salts of $\approx 10^{-13} \, {\rm mol \, cm^{-2} \, s^{-1}}$ driving the cloud droplet chemistry. An atmospheric probe can test both of these explanations by measuring the pH of the cloud droplets and the concentrations of gas-phase SO$_2$ below the clouds., Comment: Accepted for publication in The Planetary Science Journal. We kindly ask the planetary science community for feedback and comments. (67 pages, 8 Figures, 7 Tables, Full Model Output Data: https://doi.org/10.7910/DVN/AKUTME)

We study the principal core g-mode oscillation in hybrid stars containing quark matter and find that they have an unusually large frequency range ($\approx$ 200 - 600 Hz) compared to ordinary neutron stars or self-bound quark stars of the same mass. Theoretical arguments and numerical calculations that trace this effect to the difference in the behaviour of the equilibrium and adiabatic sound speeds in the mixed phase of quarks and nucleons are provided. We propose that the sensitivity of core g-mode oscillations to non-nucleonic matter in neutron stars could be due to the presence of a mixed quark-nucleon phase. Based on our analysis, we conclude that for binary mergers where one or both components may be a hybrid star, the fraction of tidal energy pumped into resonant g-modes in hybrid stars can exceed that of a normal neutron star by a factor of 2-3, although resonance occurs during the last stages of inspiral. A self-bound star, on the other hand, has a much weaker tidal overlap with the g-mode. The cumulative tidal phase error in hybrid stars, $\Delta\phi\cong$ 0.5 rad, is comparable to that from tides in ordinary neutron stars, presenting a challenge in distinguishing between the two cases. However, should the principal g-mode be excited to sufficient amplitude for detection in a post-merger remnant with quark matter in its interior, its frequency would be a possible indication for the existence of non-nucleonic matter in neutron stars., Comment: 22 pages, 16 figures

The United States is the largest distributor of legal services in the world, representing a $437 billion market. Of this, corporate legal departments pay law firms $80 billion for their services. Every month, legal departments receive and process invoices from these law firms and legal service providers. Legal invoice review is and has been a pain point for corporate legal department leaders. Complex and intricate, legal invoices often contain several hundred line-items that account for anything from tasks such as hands-on legal work to expenses such as copying, meals, and travel. The man-hours and scrutiny involved in the invoice review process can be overwhelming. Even with common safeguards in place, such as established billing guidelines, experienced invoice reviewers (typically highly paid in-house attorneys), and rule-based electronic billing tools ("e-billing"), many discrepancies go undetected. Using machine learning, our goal is to demonstrate the current flaws of, and to explore improvements to, the legal invoice review process for invoices submitted by law firms to their corporate clients. In this work, we detail our approach, applying several machine learning model architectures, for detecting anomalous invoice line-items based on their suitability in the legal case's lifecycle (modeled using a set of case-level and invoice line-item-level features). To overcome the challenge of unlabeled data, we generate a synthetic dataset which utilizes subject matter expertise ("SME") to manipulate existing records' attributes to reflect an anomalous state in the product lifecycle, and characterize our method's performance using a set of model architectures. We demonstrate how this process advances solving anomaly detection problems, specifically when the characteristics of the anomalies are well known, and offer lessons learned from applying our approach to real-world data., Comment: Revised abstract and contents

Atmosphere and ocean are coupled via air-sea interactions. The atmospheric conditions fuel the ocean circulation and its variability, but the extent to which ocean processes can affect the atmosphere at decadal time scales remains unclear. In particular, such low-frequency variability is difficult to extract from the short observational record, meaning that climate models are the primary tools deployed to resolve this question. Here, we assess how the ocean's intrinsic variability leads to patterns of upper-ocean heat content that vary at decadal time scales. These patterns have the potential to feed back on the atmosphere and thereby affect climate modes of variability, such as El Ni\~no or the Interdecadal Pacific Oscillation. We use the output from a global ocean-sea ice circulation model at three different horizontal resolutions, each driven by the same atmospheric reanalysis. To disentangle the variability of the ocean's direct response to atmospheric forcing from the variability due to intrinsic ocean dynamics, we compare model runs driven with inter-annually varying forcing (1958-2018) and model runs driven with repeat-year forcing. Models with coarse resolution that rely on eddy parameterizations, show (i) significantly reduced variance of the upper-ocean heat content at decadal time scales and (ii) differences in the spatial patterns of low-frequency variability compared with higher resolution models. Climate projections are typically done with general circulation models with coarse-resolution ocean components. Therefore, these biases affect our ability to predict decadal climate modes of variability and, in turn, hinder climate projections. Our results suggest that for improving climate projections, the community should move towards coupled climate models with higher oceanic resolution.

We compute the nucleon axial and induced pseudoscalar form factors using three ensembles of gauge configurations, generated with dynamical light quarks with mass tuned to approximately their physical value. One of the ensembles also includes the strange and charm quarks with their mass close to physical. The latter ensemble has large statistics and finer lattice spacing and it is used to obtain final results, while the other two are used for assessing volume effects. The pseudoscalar form factor is also computed using these ensembles. We examine the momentum dependence of these form factors as well as relations based on pion pole dominance and the partially conserved axial-vector current hypothesis., Comment: 25 pages and 27 figures

In this work, we investigate how the assumption of chemical equilibrium with leptons affects the deconfinement phase transition to quark matter. This is done within the framework of the Chiral Mean Field model (CMF) allowing for non-zero net strangeness, corresponding to the conditions found in astrophysical scenarios. We build 3-dimensional QCD phase diagrams with temperature, baryon chemical potential, and either charge or isospin fraction or chemical potential to show how the deconfinement region collapses to a line in the special case of chemical equilibrium, such as the one established the interior of cold catalyzed neutron stars.

Structure learning algorithms that learn the graph of a Bayesian network from observational data often do so by assuming the data correctly reflect the true distribution of the variables. However, this assumption does not hold in the presence of measurement error, which can lead to spurious edges. This is one of the reasons why the synthetic performance of these algorithms often overestimates real-world performance. This paper describes an algorithm that can be added as an additional learning phase at the end of any structure learning algorithm, and serves as a correction learning phase that removes potential false positive edges. The results show that the proposed correction algorithm successfully improves the graphical score of four well-established structure learning algorithms spanning different classes of learning in the presence of measurement error.

The quasi-PDF approach provides a path to computing parton distribution functions (PDFs) using lattice QCD. This approach requires matrix elements of a power-divergent operator in a nucleon at high momentum and one generically expects discretization effects starting at first order in the lattice spacing $a$. Therefore, it is important to demonstrate that the continuum limit can be reliably taken and to understand the size and shape of lattice artifacts. In this work, we report a calculation of isovector unpolarized and helicity PDFs using lattice ensembles with $N_f=2+1+1$ Wilson twisted mass fermions, a pion mass of approximately 370 MeV, and three different lattice spacings. Our results show a significant dependence on $a$, and the continuum extrapolation produces a better agreement with phenomenology. The latter is particularly true for the antiquark distribution at small momentum fraction $x$, where the extrapolation changes its sign., Comment: 24 pages, 21 figures. v2: additional references, discussion of systematics, and position-space comparison with phenomenology. v3: applied workaround for problem affecting Greek symbols in figures with some PDF viewers

We present a calculation of the pion quark momentum fraction, $\langle x \rangle$, and its third Mellin moment $\langle x^2 \rangle$. We also obtain directly, for the first time, $\langle x \rangle$ and $\langle x^2 \rangle$ for the kaon using local operators. We use an ensemble of two degenerate light, a strange and a charm quark ($N_f=2+1+1$) of maximally twisted mass fermions with clover improvement. The quark masses are chosen so that they reproduce a pion mass of about 260 MeV, and a kaon mass of 530 MeV. The lattice spacing of the ensemble is 0.093 fm and the lattice has a spatial extent of 3 fm. We analyze several values of the source-sink time separation within the range of $1.12-2.23$ fm to study and eliminate excited-states contributions. The necessary renormalization functions are calculated non-perturbatively in the RI$'$ scheme, and are converted to the $\overline{\rm MS}$ scheme at a scale of 2 GeV. The final values for the momentum fraction are $\langle x \rangle^\pi_{u^+}=0.261(3)_{\rm stat}(6)_{\rm syst}$, $\langle x \rangle^K_{u^+}=0.246(2)_{\rm stat}(2)_{\rm syst}$, and $\langle x \rangle^K_{s^+}=0.317(2)_{\rm stat}(1)_{\rm syst}$. For the third Mellin moments we find $\langle x^2 \rangle^\pi_{u^+}=0.082(21)_{\rm stat}(17)_{\rm syst}$, $\langle x^2 \rangle^K_{u^+}=0.093(5)_{\rm stat}(3)_{\rm syst}$, and $\langle x^2 \rangle^K_{s^+}=0.134(5)_{\rm stat}(2)_{\rm syst}$. The reported systematic uncertainties are due to excited-state contamination. We also give the ratio $\langle x^2 \rangle/\langle x \rangle$ which is an indication of how quickly the PDFs lose support at large $x$., Comment: 21 pages, 10 figures

The Republic of Cyprus is a small island in the southeast of Europe and member of the European Union. The first wave of COVID-19 in Cyprus started in early March, 2020 (imported cases) and peaked in late March-early April. The health authorities responded rapidly and rigorously to the COVID-19 pandemic by scaling-up testing, increasing efforts to trace and isolate contacts of cases, and implementing measures such as closures of educational institutions, and travel and movement restrictions. The pandemic was also a unique opportunity that brought together experts from various disciplines including epidemiologists, clinicians, mathematicians, and statisticians. The aim of this paper is to present the efforts of this new, multidisciplinary research team in modelling the COVID-19 pandemic in the Republic of Cyprus.