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The paper presents a modified formulation of least-squares collocation. This residual least-squares collocation (RLSC) includes a remove–compute–restore procedure with a high-resolution global geopotential model (GGM) and a topographic gravitational potential model. In contrast to previous approaches, in RLSC, the remaining input residuals are modeled with error covariance matrices instead of signal covariance matrices. Therefore, we include the full variance–covariance information of a high-resolution GGM, namely the XGM2016, to the procedure. The included covariance matrices are anisotropic and location-dependent and enable a realistic error modeling of a target area. This fact represents an advantage over covariance matrices derived from signal degree variances or empirical covariance fitting. Additionally, due to the stochastic modeling of all involved components, RLSC provides realistic accuracy estimates. In a synthetic closed-loop test case with a realistic data distribution in the Andes we demonstrate the advantages of RLSC for regional geoid modeling and quantify the benefit which results mainly from a rigorously handled high-resolution GGM. In terms of root mean square deviations from the true reference solution, RLSC delivers an improvement of about 30% compared to a standard LSC approach, where the benefit is particularly pronounced in areas with a sparse data distribution. This improved performance, together with the fact that the resulting stochastic error estimates better reflect the true errors, might be an important aspect for the application of RLSC to derive gravity potential values and their uncertainties at reference stations of the international height reference system.

Various types of heterogeneous observations can be combined within a parameter estimation process using spherical radial basis functions (SRBFs) for regional gravity field refinement. In this process, regularization is in most cases inevitable, and choosing an appropriate value for the regularization parameter is a crucial issue. This study discusses the drawbacks of two frequently used methods for choosing the regularization parameter, which are the L-curve method and the variance component estimation (VCE). To overcome their drawbacks, two approaches for the regularization parameter determination are proposed, which combine the L-curve method and VCE. The first approach, denoted as “VCE-Lc”, starts with the calculation of the relative weights between the observation techniques by means of VCE. Based on these weights, the L-curve method is applied to determine the regularization parameter. In the second approach, called “Lc-VCE”, the L-curve method determines first the regularization parameter, and it is set to be fixed during the calculation of the relative weights between the observation techniques from VCE. To evaluate and compare the performance of the two proposed methods with the L-curve method and VCE, all these four methods are applied in six study cases using four types of simulated observations in Europe, and their modeling results are compared with the validation data. The RMS errors (w.r.t the validation data) obtained by VCE-Lc and Lc-VCE are smaller than those obtained from the L-curve method and VCE in all the six cases. VCE-Lc performs the best among these four tested methods, no matter if using SRBFs with smoothing or non-smoothing features. These results prove the benefits of the two proposed methods for regularization parameter determination when different data sets are to be combined.

An airborne gravity survey for Nepal was carried out in December 2010 with the primary goal to provide data for a new national geoid model, which will in turn provide gravity information for the future global gravity field EGM2020. This gravity data is used again to determine the regional geoid model (NPG20) for Nepal using Least-Squares Collocation (LSC) with Remove-Compute-Restore approach. In comparison to the previously computed geoid model, Nepal Geoid 2011 (NPG11) using EGM2008, this study applies XGM2019e as the global model. The comparative study shows, XGM2019e fits the airborne gravity observations much better than EGM2008 in the study area. The computation of geoid heights is done using LSC with the determination of proper covariance function for the gravity data, while the previous study includes a combination of LSC for downward continuation and spherical FFT for the calculation of the geoid. This contribution evaluates the benefit of our two main adaptions. The comparative study of geoids, NPG11 and NPG20 showed that there exist significant differences between these models especially in the area where the elevation is higher than 7000 m. The data analysis of the study showed that the currently available airborne gravity data was not sufficient to provide high frequency gravity signals and the significant differences in these geoid models was solely related to the different handling of the high-frequency gravity field component of the background model, i.e., EGM2008 and XGM2019e.

The primary objective of the 1-cm geoid experiment in Colorado (USA) is to compare the numerous geoid computation methods used by different groups around the world. This is intended to lay the foundations for tuning computation methods to achieve the sought after 1-cm accuracy, and also evaluate how this accuracy may be robustly assessed. In this experiment, (quasi)geoid models were computed using the same input data provided by the US National Geodetic Survey (NGS), but using different methodologies. The rugged mountainous study area (730 km × 560 km) in Colorado was chosen so as to accentuate any differences between the methodologies, and to take advantage of newly collected GPS/leveling data of the Geoid Slope Validation Survey 2017 (GSVS17) which are now available to be used as an accurate and independent test dataset. Fourteen groups from fourteen countries submitted a gravimetric geoid and a quasigeoid model in a 1′ × 1′ grid for the study area, as well as geoid heights, height anomalies, and geopotential values at the 223 GSVS17 marks. This paper concentrates on the quasigeoid model comparison and evaluation, while the geopotential value investigations are presented as a separate paper (Sánchez et al. in J Geodesy 95(3):1. https://doi.org/10.1007/s00190-021-01481-0 , 2021). Three comparisons are performed: the area comparison to show the model precision, the comparison with the GSVS17 data to estimate the relative accuracy of the models, and the differential quasigeoid (slope) comparison with GSVS17 to assess the relative accuracy of the height anomalies at different baseline lengths. The results show that the precision of the 1′ × 1′ models over the complete area is about 2 cm, while the accuracy estimates along the GSVS17 profile range from 1.2 cm to 3.4 cm. Considering that the GSVS17 does not pass the roughest terrain, we estimate that the quasigeoid can be computed with an accuracy of ~ 2 cm in Colorado. The slope comparisons show that RMS values of the differences vary from 2 to 8 cm in all baseline lengths. Although the 2-cm precision and 2-cm relative accuracy have been estimated in such a rugged region, the experiment has not reached the 1-cm accuracy goal. At this point, the different accuracy estimates are not a proof of the superiority of one methodology over another because the model precision and accuracy of the GSVS17-derived height anomalies are at a similar level. It appears that the differences are not primarily caused by differences in theory, but that they originate mostly from numerical computations and/or data processing techniques. Consequently, recommendations to improve the model precision toward the 1-cm accuracy are also given in this paper.

In this paper, we report on the direct positioning of small multi-directional radar reflectors, so-called octahedrons, with the synthetic aperture radar (SAR) satellite TerraSAR-X. Its highest resolution imaging mode termed staring spotlight enables the use of such octahedron reflectors with a dimension of only half a meter, but still providing backscatter equivalent to 1–2 cm observation error. Four octahedrons were deployed at Wettzell geodetic observatory, and observed by TerraSAR-X with 12 acquisitions in three different geometries. By applying our least squares stereo SAR algorithm already tested with common trihedral corner reflectors (CRs), and introducing a novel differential extension using one octahedron as reference point, the coordinates of the remaining octahedrons were directly retrieved in the International Terrestrial Reference Frame (ITRF). Contrary to our standard processing, the differential approach does not require external corrections for the atmospheric path delays and the geodynamic displacements, rendering it particularly useful for joint geodetic networks employing SAR and GNSS. In this paper, we present and discuss both methods based on results when applying them to the aforementioned Wettzell data set of the octahedrons. The comparison with the independently determined reference coordinates confirms the positioning accuracy with 2–5 cm for the standard approach, and 2–3 cm for the differential processing. Moreover, we present statistical uncertainty estimates of the observations and the positioning solutions, which are additionally provided by our parameter estimation algorithms. The results also include our 1.5 m CR available at Wettzell, and the outcomes clearly demonstrate the advantage of the multi-directional octahedrons over conventional CRs for global positioning applications with SAR.

The rate at which HIV-1 infected individuals progress to AIDS is highly variable and impacted by T cell immunity. CD8 T cell inhibitory molecules are up-regulated in HIV-1 infection and associate with immune dysfunction. We evaluated participants (n = 122) recruited to the SPARTAC randomised clinical trial to determine whether CD8 T cell exhaustion markers PD-1, Lag-3 and Tim-3 were associated with immune activation and disease progression. Expression of PD-1, Tim-3, Lag-3 and CD38 on CD8 T cells from the closest pre-therapy time-point to seroconversion was measured by flow cytometry, and correlated with surrogate markers of HIV-1 disease (HIV-1 plasma viral load (pVL) and CD4 T cell count) and the trial endpoint (time to CD4 count <350 cells/μl or initiation of antiretroviral therapy). To explore the functional significance of these markers, co-expression of Eomes, T-bet and CD39 was assessed. Expression of PD-1 on CD8 and CD38 CD8 T cells correlated with pVL and CD4 count at baseline, and predicted time to the trial endpoint. Lag-3 expression was associated with pVL but not CD4 count. For all exhaustion markers, expression of CD38 on CD8 T cells increased the strength of associations. In Cox models, progression to the trial endpoint was most marked for PD-1/CD38 co-expressing cells, with evidence for a stronger effect within 12 weeks from confirmed diagnosis of PHI. The effect of PD-1 and Lag-3 expression on CD8 T cells retained statistical significance in Cox proportional hazards models including antiretroviral therapy and CD4 count, but not pVL as co-variants. Expression of 'exhaustion' or 'immune checkpoint' markers in early HIV-1 infection is associated with clinical progression and is impacted by immune activation and the duration of infection. New markers to identify exhausted T cells and novel interventions to reverse exhaustion may inform the development of novel immunotherapeutic approaches.

T cell dysfunction occurs early following HIV infection, impacting the emergence of non-AIDS morbidities and limiting curative efforts. ART initiated during primary HIV infection (PHI) can reverse this dysfunction, but the extent of recovery is unknown. We studied 66 HIV-infected individuals treated from early PHI with up to three years of ART. Compared with HIV-uninfected controls, CD4 and CD8 T cells from early HIV infection were characterised by T cell activation and increased expression of the immune checkpoint receptors (ICRs) PD1, Tim-3 and TIGIT. Three years of ART lead to partial – but not complete – normalisation of ICR expression, the dynamics of which varied for individual ICRs. For HIV-specific cells, epigenetic profiling of tetramer-sorted CD8 T cells revealed that epigenetic features of exhaustion typically seen in chronic HIV infection were already present early in PHI, and that ART initiation during PHI resulted in only a partial shift of the epigenome to one with more favourable memory characteristics. These findings suggest that although ART initiation during PHI results in significant immune reconstitution, there may be only partial resolution of HIV-related phenotypic and epigenetic changes.

Mucosal-associated invariant T (MAIT) cells are abundant in humans and recognize bacterial ligands. Here, we demonstrate that MAIT cells are also activated during human viral infections in vivo . MAIT cells activation was observed during infection with dengue virus, hepatitis C virus and influenza virus. This activation—driving cytokine release and Granzyme B upregulation—is TCR-independent but dependent on IL-18 in synergy with IL-12, IL-15 and/or interferon-α/β. IL-18 levels and MAIT cell activation correlate with disease severity in acute dengue infection. Furthermore, HCV treatment with interferon-α leads to specific MAIT cell activation in vivo in parallel with an enhanced therapeutic response. Moreover, TCR-independent activation of MAIT cells leads to a reduction of HCV replication in vitro mediated by IFN-γ. Together these data demonstrate MAIT cells are activated following viral infections, and suggest a potential role in both host defence and immunopathology. Mucosal Associated Invariant T cells have been implicated in response to bacterial pathogens. Here the authors show that in human viral infections, these cells are activated by IL-18 in cooperation with other pro-inflammatory cytokines, producing interferon gamma and granzyme B.

Purpose In tendon research, using ultrasound (US), studies often refer to tendon thickness, structural abnormalities and neovascularisation. The reliability concerning these measurements and evaluations is seldom reported. The aim of this study was to assess the intra- and inter-observer reliability for quantitative measures (thickness) and qualitative evaluations (structure and neovascularisation) of symptomatic and asymptomatic Achilles and patellar tendons with US and colour Doppler using a modified Öhberg score. Methods Twenty-eight consecutive patients with symptomatic and asymptomatic Achilles ( n  = 27) and patellar tendons ( n  = 26) were included. Tendon anteroposterior thickness was measured. Tendon structure and neovascularisation were evaluated using a modified Öhberg score. US-images were evaluated twice by four independent observers. Results Mean thickness for Achilles and patellar tendons was 8.4 mm (±2.0) and 5.5 mm (±1.7), respectively. The reliability for measures of distance was high all over (ICC = 0.963–0.999). A moderate-strong correlation was found between observers concerning evaluation of neovascularisation ( r  = 0.767–0.992) and poor-moderate correlation concerning evaluation of structural changes ( r  = 0.379–0.837). Intra-observer reliability was moderate strong for evaluations of both tendon structure ( k  = 0.537–0.873) and neovascularisation ( k  = 0.639–0.864). Conclusions With a strict method for how to measure tendon thickness and set criteria for evaluating structural changes and amount and distribution of neovascularisation, US and colour Doppler is a reliable method for evaluating Achilles and patellar tendons. The modified, 4-graded, Öhberg score was found to be a reproducible instrument for assessment of tendon structure and neovascularisation.

Treatment of HIV-1 infection with antiretroviral therapy (ART) in the weeks following transmission may induce a state of ‘post-treatment control’ (PTC) in some patients, in whom viraemia remains undetectable when ART is stopped. Explaining PTC could help our understanding of the processes that maintain viral persistence. Here we show that immunological biomarkers can predict time to viral rebound after stopping ART by analysing data from a randomized study of primary HIV-1 infection incorporating a treatment interruption (TI) after 48 weeks of ART (the SPARTAC trial). T-cell exhaustion markers PD-1, Tim-3 and Lag-3 measured prior to ART strongly predict time to the return of viraemia. These data indicate that T-cell exhaustion markers may identify those latently infected cells with a higher proclivity to viral transcription. Our results may open new avenues for understanding the mechanisms underlying PTC, and eventually HIV-1 eradication. In some HIV-1-infected individuals, viraemia remains undetectable after antiretroviral treatment, but which of these patients will experience viral rebound is difficult to predict. Here the authors show that T cell exhaustion markers before treatment are predictive of shorter time to viral rebound.