Weak Constraints Research Articles

Morphomechanics of growing curled petals and leaves

Petals and leaves are usually curled and exhibit intriguing morphology evolution upon growth, which contributes to their important biological functions. To understand the underlying morphoelastic mechanism and to determine the crucial factors that govern the growth-induced instability patterning in curved petals and leaves, we develop an active thin shell model that can describe variable curvatures and spontaneous growth, within the framework of general differential geometry based on curvilinear coordinates and hyperelastic deformation theory. Analytical solutions of distinguished growing shapes such as saddle surface and cylindrical mode are then derived. We reveal distinct morphological evolutions of doubly curved leaves/petals with different curvatures κx (along the main vein) and κy (perpendicular to the main vein) upon differential growth. Compared to the flat (zero curvature) configuration, leaves/petals with longitudinal curvature κx experience a global bending deformation. With the increase of growth strain, the leaf/petal undergoes a coupling behavior of edge wrinkling and global bending deformation, associated with a pitchfork bifurcation. Conversely, the transverse curvature κy does not lead to significant bending behavior, but results in delayed critical buckling threshold and reduced wrinkling amplitude. Physical insights into curvature effects on morphology evolutions are further provided by the analysis of nonlinear competition between bending and membrane energies. Moreover, we explore the effect of vein constraint on pattern formation, showing that, unlike the edge wrinkling observed in leaves with strong vein constraint, those with weak vein constraint are prone to grow into a saddle shape, consistent with analytical solutions. The results uncover the intricate interplay between configurational curvature and vein confinement on plant morphogenesis, providing fundamental insights into a variety of growing shapes of curled petals and leaves.

Bayesian recalibration of Planck galaxy cluster scaling relations including relativistic Sunyaev-Zel’dovich corrections

Abstract We investigate the impact of relativistic SZ corrections on Planck measurements of massive galaxy clusters, finding that they have a significant impact at the $\approx$ 5–15% and up to $\approx$ 3 $\sigma$ level. We investigate the possibility of constraining temperature directly from these SZ measurements but find that only weak constraints are possible for the most significant detections; for most clusters, an external temperature measurement is required to correctly measure integrated Compton-y. We also investigate the impact of profile shape assumptions and find that these have a small but non-negligible impact on measured Compton-y, at the $\approx$ 5% level. Informed by the results of these investigations, we recalibrate the Planck SZ observable-mass scaling relation, using the updated NPIPE data release and a larger sample of X-ray mass estimates. Along with the expected change in the high-mass end of the scaling relation, which does not impact Planck mass estimation, we also find hints of a low-mass deviation, but this requires better understanding of the selection function in order to confirm.

Foreign executives, digital transformation, and innovation performance: Evidence from Chinese-listed firms.

This study investigates the effect of foreign executives on firms' innovation performance and the mediation role of digital transformation in Chinese-listed firms from 2011 to 2021. Our findings indicate that the presence of foreign executives in top management teams promotes firms' innovation performance by enhancing digital transformation. Further analyses show that foreign executives contribute significantly to improving firms' radical innovation performance rather than incremental innovation performance. We also examine the moderating effect of negative performance feedback and financing constraints between foreign executives and innovation performance, finding that foreign executives can promote innovation performance particularly in firms with negative performance feedback and weak financing constraints.

Constraints on dark energy from TDCOSMO & SLACS lenses

ABSTRACT Problems with the cosmological constant model of dark energy motivate the investigation of alternative scenarios. I make the first measurement of the dark energy equation of state using the hierarchical strong lensing time delay likelihood provided by TDCOSMO. I find that the combination of seven TDCOSMO lenses and 33 SLACS lenses is only able to provide a weak constraint on the dark energy equation of state, w < −1.75 at 68 per cent confidence, which nevertheless implies the presence of a phantom dark energy component. When the strong lensing time delay data is combined with a collection of cosmic microwave background, baryon acoustic oscillation and Type Ia supernova data, I find that the equation of state is w = −1.025 ± 0.029.

Atmospheres as a window to rocky exoplanet surfaces

ABSTRACT As the characterization of exoplanet atmospheres proceeds, providing insights into atmospheric chemistry and composition, a key question is how much deeper into the planet we might be able to see from its atmospheric properties alone. For small planets with modest atmospheres and equilibrium temperatures, the first layer below the atmosphere will be their rocky surface. For such warm rocky planets, broadly Venus-like planets, the high temperatures and moderate pressures at the base of their atmospheres may enable thermochemical equilibrium between rock and gas. This links the composition of the surface to that of the observable atmosphere. Using an equilibrium chemistry code, we find a boundary in surface pressure–temperature space which simultaneously separates distinct mineralogical regimes and atmospheric regimes, potentially enabling inference of surface mineralogy from spectroscopic observations of the atmosphere. Weak constraints on the surface pressure and temperature also emerge. This regime boundary corresponds to conditions under which SO2 is oxidized and absorbed by calcium-bearing minerals in the crust, thus the two regimes reflect the sulphidation of the crust. The existence of these atmospheric regimes for Venus-like planets is robust to plausible changes in the elemental composition. Our results pave the way to the prospect of characterizing exoplanetary surfaces as new data for short period rocky planet atmospheres emerge.

FACTS placement for reactive power planning with weak node constraints using an improved symbiotic search algorithm

In this paper, an economically feasible and reliable operation of the IEEE 57 bus system for Optimal Power Flow (OPF) is proposed. The Improved Symbiotic Organisms Search (ISOS) algorithm is proposed for effective reactive power planning as an OPF issue. Further, the optimal position of Flexible AC Transmission Systems (FACTS) is taken into consideration, by including the existing system controlling variables like reactive power generators output, transformer tapping and capacitors connected at shunt. The objective of the work is two-fold; i.e., to reduce the energy loss and to enhance the voltage profile within the prescribed limit by ensuring the economic operation and investment cost of FACTS in the system. In this work, two FACTS devices like Static Var Compensator (SVC) and Thyristor-Controlled Series Controller (TCSC) have been taken into consideration. Voltage sensitivity indicator and reactive power flow are two tools that are utilised in order to locate weak nodes for the implementation of FACTS. Finally, the performance of the ISOS algorithm is compared with that of three other state- of-the -art optimization techniques, such as, Symbiotic Organisms Search (SOS), Differential Evolution (DE) and Teaching Learning Based Optimization (TLBO). A Non-parametric statistical analysis is also performed to investigate the dominance of the ISOS algorithm over others.

Photodynamical Modeling of the Compact, Multiply Eclipsing Systems KIC 5255552, KIC 7668648, KIC 10319590, and EPIC 220204960

We present photodynamical models of four eclipsing binary systems that show strong evidence of being members of higher-order multiple systems via their strong eclipse timing variations and/or via the presence of extra eclipse events. Three of these systems are from the main Kepler mission, and the other is from the K2 mission. We provide some ground-based radial velocities measurements for the three Kepler systems and make use of recent light curves from the TESS mission. Our sample consists of two 2 + 1 systems and two 2 + 2 systems. The first 2 + 1 system, KIC 7668648, consists of an eclipsing binary (Pbin = 27.8 days) with late-type stars (M1=0.8403±0.0090M⊙, R1=1.0066±0.0036R⊙ and M2=0.8000±0.0085M⊙, R2=0.8779±0.0032R⊙) with a low-mass star (M3=0.2750±0.0029M⊙, R3=0.2874±0.0010R⊙) on a roughly coplanar outer orbit (P3=208 days). There are several eclipse events involving the third star that allow for the precise determination of the system parameters. The second 2 + 1 system, KIC 10319590, consists of a binary (Pbin=21.3 days) with late-type stars (M1=1.108±0.043M⊙, R1=1.590±0.019R⊙ and M2=0.743±0.023M⊙, R2=0.7180±0.0086R⊙) that stopped eclipsing about a third of the way into the nominal Kepler mission. We show here that the third star in this system is a Sun-like star (M3=1.049±0.038M⊙, R3=1.39±0.11R⊙) on an inclined outer orbit (P3=456 days). In this case, there are no extra eclipse events. We present the first comprehensive solution for KIC 5255552 and demonstrate that it is a 2 + 2 system consisting of an eclipsing binary (Pbin,1=32.5 days) with late-type stars (M1=0.950±0.018M⊙, R1=0.9284±0.0063R⊙ and M2=0.745±0.014M⊙, R2=0.6891±0.0051R⊙) paired with a non-eclipsing binary (Pbin,2=33.7 days) with somewhat lower-mass stars (M3=0.483±0.010M⊙, R3=0.4640±0.0036R⊙ and M4=0.507±0.010M⊙, R4=0.4749±0.0031R⊙). The two binaries, which have nearly coplanar orbits, orbit their common barycenter on a roughly aligned outer orbit (Pout=878 days). There are extra eclipse events involving the component stars of the non-eclipsing binary, which leads to relatively small uncertainties in the system parameters. The second 2 + 2 system, EPIC 220204960, consists of a pair of eclipsing binaries (Pbin,2=13.3 days, Pbin,2=14.4 days) that both consist of two low-mass stars (M1=0.54M⊙, R1=0.46R⊙, M2=0.46M⊙, R2=0.37R⊙ and M3=0.38M⊙, R3=0.40R⊙, M4=0.38M⊙, R4=0.37R⊙) that orbit their common barycenter on a poorly determined outer orbit. Because of the relatively short time span of the observations (≈80 days for the photometry and ≈70 days for the radial velocity measurements), the masses and radii of the four stars in EPIC 220204960 can only be determined with accuracies of ≈10% and ≈5%, respectively. We show that the most likely period of the outer orbit is 957 days, with a 1σ range of 595 to 1674 days. We can only place weak constraints on the mutual inclinations of the orbital planes, and additional radial velocity measurements and/or additional eclipse observations would allow for much tighter constraints on the properties of the outer orbit.

Detection of Low-Velocity Layer Using Passive Surface-Wave Data and Deep Learning: An Application in The Urban Area of Hangzhou, China

Passive surface-wave methods using dense seismic arrays have gained growing attention in near-surface high-resolution imaging in urban environments. Deep learning (DL) can release a tremendous workload brought by dense seismic arrays. We presented a case study of shear-wave velocity (Vs) structure imaging in the Hangzhou urban area (eastern China) using DL inversion. Noise data were recorded by dense linear arrays with approximately 5 m spacing deployed along two crossing roads for investigating the top 80 m of the subsurface. Phase-velocity dispersion curves are extracted from virtual shot gathers using multichannel analysis of surface waves. We divided the area where the low-velocity layer (LVL) may exist into three layers with a thickness of 5 m. We gave the four layers weak constraints to generate training dataset and adopted a convolutional neural network to directly invert fundamental-mode Rayleigh-wave phase velocity for 1D Vs models. To improve the accuracy, we further applied the sensitivities to weight the loss function in DL inversion. The obtained pseudo-2D Vs profiles correspond to the velocities estimated from logging data and previous survey. The well-trained neural network successfully identified that the LVL is located at 50-60 m deep. And this network was also achieved accurately the inversion of a dense seismic network nearby. The results of this survey demonstrate the accuracy and efficiency of delineating near-surface structures from traffic-induced noise using the DL technique, which has great potential for monitoring subsurface changes in urban areas.

The DESI One-Percent Survey: exploring a generalized SHAM for multiple tracers with the UNIT simulation

ABSTRACT We perform SubHalo Abundance Matching (SHAM) studies on UNIT simulations with {σ, Vceil, vsmear}-SHAM and {σ, Vceil, fsat}-SHAM. They are designed to reproduce the clustering on 5–30 $\, {\, h^{-1}\, {\rm Mpc}}$ of luminous red galaxies (LRGs), emission-line galaxies (ELGs), and quasi-stellar objects (QSOs) at 0.4 < z < 3.5 from DESI (Dark Energy Spectroscopic Instrument) One Percent Survey. Vceil is the incompleteness of the massive host (sub)haloes and is the key to the generalized SHAM. vsmear models the clustering effect of redshift uncertainties, providing measurements consistent with those from repeat observations. A free satellite fraction fsat is necessary to reproduce the clustering of ELGs. We find ELGs present a more complex galaxy–halo mass relation than LRGs reflected in their weak constraints on σ. LRGs, QSOs, and ELGs show increasing Vceil values, corresponding to the massive galaxy incompleteness of LRGs, the quenched star formation of ELGs and the quenched black hole accretion of QSOs. For LRGs, a Gaussian vsmear presents a better profile for subsamples at redshift bins than a Lorentzian profile used for other tracers. The impact of the statistical redshift uncertainty on ELG clustering is negligible. The best-fitting satellite fraction for DESI ELGs is around 4 per cent, lower than previous estimations for ELGs. The mean halo mass log10(〈Mvir〉) in ${{\, h^{-1}\, \mbox{M}_\odot }}{}$ for LRGs, ELGs, and QSOs are 13.16 ± 0.01, 11.90 ± 0.06, and 12.66 ± 0.45, respectively. Our generalized SHAM algorithms facilitate the production of multitracer galaxy mocks for cosmological tests.

Performance of Common Scene Stacking Atmospheric Correction on Nonlinear InSAR Deformation Retrieval

Atmospheric Phase Screen (APS) is a major noise that suppresses the accuracy of InSAR deformation time series products. Several correction methods have been developed to perform APS reduction in the InSAR analysis, in which an algorithm called Common Scene Stacking (CSS) method draws wide attention in the community as the method was supposed to effectively separate atmospheric contributions without any external data. CSS was initially proposed for solving linearly interseismic deformation. Whether CSS can be applied in nonlinear deformation cases remains unsolved. In this study, we first conduct a series of data simulations including variable elastic deformation components and also propose an iterative strategy to address the inherent weak edge constraint issues in CSS under different deformation conditions. The results show that signal-to-noise ratio (SNR) is a key parameter affecting the performance of CSS in APS separation. For example, the recovery rate of deformation can generally be greater than 80% from datasets with SNR greater than 10 dB. Our results imply that CSS can favor further improvement of InSAR measurement accuracy. The proposed method in this study was applied to assessing deformation history across the 2020 Mw 5.7 Dingjie earthquake, in which logarithmic postseismic deformation history and coseismic contribution can be successfully retrieved once.

OGLE-2019-BLG-1180Lb: Discovery of a Wide-orbit Jupiter-mass Planet around a Late-type Star

We report on the discovery and analysis of the planetary microlensing event OGLE-2019-BLG-1180 with a planet-to-star mass ratio q ∼ 0.003. The event OGLE-2019-BLG-1180 has unambiguous cusp-passing and caustic-crossing anomalies, which were caused by a wide planetary caustic with s ≃ 2, where s is the star–planet separation in units of the angular Einstein radius θ E. Thanks to well-covered anomalies by the Korea Micorolensing Telescope Network (KMTNet), we measure both the angular Einstein radius and the microlens parallax in spite of a relatively short event timescale of t E = 28 days. However, because of a weak constraint on the parallax, we conduct a Bayesian analysis to estimate the physical lens parameters. We find that the lens system is a super-Jupiter-mass planet of orbiting a late-type star of at a distance . The projected star–planet separation is , which means that the planet orbits at about four times the snow line of the host star. Considering the relative lens–source proper motion of μ rel = 6 mas yr−1, the lens will be separated from the source by 60 mas in 2029. At that time one can measure the lens flux from adaptive optics imaging of Keck or a next-generation 30 m class telescope. OGLE-2019-BLG-1180Lb represents a growing population of wide-orbit planets detected by KMTNet, so we also present a general investigation into prospects for further expanding the sample of such planets.

Finite element simulation and strength evaluation on innovative and traditional composite shear wall systems

SummaryComposite shear wall (CSW) system, which consists of a steel boundary frame and a steel panel with a reinforced concrete (RC) panel attached to one side of it using bolts, is commonly used in mid‐ to high‐rise buildings. In a CSW system, RC panel functions as out‐of‐plane restraint to prevent overall buckling of steel panel, thereby enhancing system behavior. However, for a traditional CSW system, the RC panel is in direct contact with the steel boundary frame. The RC panel tends to crush under seismic loading, thereby leading to a weak constraint to steel panel buckling. The innovative CSW system, where a gap remained between steel boundary frame and RC panel, demonstrated better cyclic behavior than the traditional CSW system. Current studies aimed to investigate cyclic behavior, parameter effects, and determination of RC panel stiffness of CSW systems. In this paper, detailed FE models were developed for simulating cyclic behavior of both innovative and traditional CSW systems and validated by test results. FE models accurately predicted lateral load‐drift response and failure patterns of both innovative and traditional CSW systems. System failure patterns and load‐carrying mechanism of RC panels were discussed. The effects of major parameters, including steel panel thickness, RC panel thickness, ratio of bolt spacing to steel panel thickness, and gap between frame and RC panel, were examined using the validated models. Simulation results indicated that steel panel thickness contributed to increase the lateral strength and initial stiffness of both innovative and traditional CSW systems. Although RC panel thickness, ratio of bolt spacing to steel panel thickness, and gap between frame and RC panel had negligible effects on system strength and stiffness, they should also be carefully designed to ensure local stability of the steel panel and system ductility. Formulations were proposed for predicting the lateral strength of both innovative and traditional CSW systems. The average difference between calculated and test/simulated lateral strength was less than 3%.

The adaptive stochasticity hypothesis: Modeling equifinality, multifinality, and adaptation to adversity

Neural phenotypes are the result of probabilistic developmental processes. This means that stochasticity is an intrinsic aspect of the brain as it self-organizes over a protracted period. In other words, while both genomic and environmental factors shape the developing nervous system, another significant-though often neglected-contributor is the randomness introduced by probability distributions. Using generative modeling of brain networks, we provide a framework for probing the contribution of stochasticity to neurodevelopmental diversity. To mimic the prenatal scaffold of brain structure set by activity-independent mechanisms, we start our simulations from the medio-posterior neonatal rich club (Developing Human Connectome Project, n = 630). From this initial starting point, models implementing Hebbian-like wiring processes generate variable yet consistently plausible brain network topologies. By analyzing repeated runs of the generative process (>107 simulations), we identify critical determinants and effects of stochasticity. Namely, we find that stochastic variation has a greater impact on brain organization when networks develop under weaker constraints. This heightened stochasticity makes brain networks more robust to random and targeted attacks, but more often results in non-normative phenotypic outcomes. To test our framework empirically, we evaluated whether stochasticity varies according to the experience of early-life deprivation using a cohort of neurodiverse children (Centre for Attention, Learning and Memory; n = 357). We show that low-socioeconomic status predicts more stochastic brain wiring. We conclude that stochasticity may be an unappreciated contributor to relevant developmental outcomes and make specific predictions for future research.

UAMD-Net: A Unified Adaptive Multimodal Neural Network for Dense Depth Completion

Depth estimation is a critical problem in robotics applications especially autonomous driving. Currently, depth prediction based on binocular stereo matching and depth completion based on fusion of monocular image and laser point cloud are two mainstream methods. However, the former usually suffers from lack of constraint while building cost volume, and the latter could not be trained in self-supervised way and haven’t utilized the geometric constraint of stereo matching, which we think will further improve the performance. Therefore, we propose a novel multimodal neural network, namely UAMD-Net, for dense depth completion based on fusion of binocular stereo matching and the weak constraint from the sparse point clouds. Specifically, the sparse point clouds are converted to sparse depth map and filled to the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">multimodal feature encoder</i> (MFE) with binocular image, constructing a cross-modal cost volume. Then, it will be further processed by the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">multimodal feature aggregator</i> (MFA) and the depth regression layer. Furthermore, since previous multimodal depth estimation methods ignore the problem of modality dependence, we propose a new training strategy called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">random modality dropout</i> (RMD) which enables the network to be adaptively trained with multiple modality inputs and inference with specific modality inputs. Benefiting from the flexible network structure and adaptive training method, our proposed network can realize unified training under various modality input conditions. Comprehensive experiments conducted on KITTI and DrivingStereo depth completion datasets demonstrate that our method produces robust results and outperforms other state-of-the-art methods.

Association Between Directors With Foreign Experience and Firms’ Environmental Disclosure

Environmental concerns garner global attention, with firms in developing nations responsible for addressing these issues effectively. Environmental disclosure is a prominent aspect of this responsibility, which has become crucial to corporate practice in these nations. This study explores directors’ foreign experience’s influence on a firm’s environmental information disclosure. Data from listed firms in China, a developing country, are employed for this analysis. Using an empirical model, we investigate the proposed hypotheses. The results indicate a trend among firms to favor directors with foreign experience, given their apparent inclination toward environmental information disclosure. However, it’s been observed that corporate governance tends to weaken the positive correlation between hiring directors with foreign experience and environmental information disclosure. This positive association is particularly evident in firms with weak financing constraints, those subjected to strict environmental regulations, and state-owned enterprises. Our study offers valuable insights for managers and decision-makers in developing countries, particularly regarding managing corporate social responsibility and facilitating green transitions in response to environmental regulations. It aids top-tier management in bolstering their internal strategies to optimize their contribution to environmental sustainability. This study, therefore, presents a valuable exploration into the role of directors with foreign experience in influencing firms’ environmental information disclosure.

S689 Fiber, Antispasmodics, and Laxatives Remain the Mainstay of IBS Treatment: A Potential Consequence of Weak Guideline Recommendations, Time Constraints, and High Drug Costs

S689 Fiber, Antispasmodics, and Laxatives Remain the Mainstay of IBS Treatment: A Potential Consequence of Weak Guideline Recommendations, Time Constraints, and High Drug Costs

Determination of single crystal thermal expansion in Uranium-6wt%Niobium shape memory alloy using in-situ diffraction and modeling of textured polycrystalline samples

In-situ neutron diffraction and ex-situ dilatometry experiments were performed on a chemically banded, quenched uranium-6wt% niobium shape memory alloy to study the impact of deformation-(detwinning-) induced texture on the evolution of thermally induced strains (and associated stresses). Thermal heating and cooling cycles between 5K and 473K were performed in-situ with neutron diffraction, and the lattice strain evolution is reported for the observed monoclinic α″ phase. Comparisons between the measured diffraction strains and macroscopic dilatometry experiments reveal relationships between micro- and macro-level thermal expansion. Softening of the texture during heating suggests that twin boundary motion can accommodate the large internal thermal strains which are approximately 2% greater than that typically observed during the 175K heating interval used to age more randomly oriented polycrystalline material. Assuming weak constraint of neighboring grains in randomly textured polycrystals, the single crystal thermal expansion tensor is extracted from measurements of lattice strains over the range 5K to 473K. Predictions of polycrystalline thermal expansion, based upon this single crystal thermal expansion tensor, are shown to compare favorably with bulk thermal expansion observations of the as quenched microstructure. However, such a lower-bound estimate is insufficient to explain all aspects of the behavior of the textured material, where the matrix is not isotropic. It is hypothesized that relaxation processes which occur within the quenched microstructure during heating are responsible for the distinct thermal expansion behavior observed during the initial heating cycle compared to cooling and subsequent cycling.

Deontic Paradoxes in ASP with Weak Constraints

Deontic Paradoxes in ASP with Weak Constraints

Administrative monopoly regulation and corporate tax avoidance - evidence from China

This study examines the impact of administrative monopoly regulation on corporate tax avoidance. Using the difference-in-difference (DID) methodology and data from A-share listed companies for the period 2012–2020, we find that China's Fair Competition Review System (FCRS) significantly reduces tax avoidance by administrative monopolies. Possible channels include increasing analyst attention, improving quality of corporate disclosure, and increasing management ownership. The enhanced external monitoring and increased internal incentives resulting from the implementation of the FCRS reduce the tax avoidance impulse of administrative monopolies. Heterogeneity analysis shows that the dampening effect of the FCRS on tax avoidance is more pronounced among firms with strong short-term solvency, weak financing constraints, and defect-free internal controls.

Weak constraint 4D-Var data assimilation in the Regional Ocean Modeling System (ROMS) using a saddle-point algorithm: Application to the California Current Circulation

The saddle-point formulation of weak constraint 4-dimensional variational (4D-Var) data assimilation has been developed for the Regional Ocean Modeling System (ROMS), and is applied here to the California Current System (CCS). Unlike the conventional primal and dual forcing formulation of weak constraint 4D-Var, the saddle-point formulation can be efficiently parallelized in time, leading to a substantial decrease in wall-clock run time. The performance of the ROMS saddle-point 4D-Var algorithm is assessed here and compared to that of the dual forcing formulation which is the current standard in ROMS. While the rate of convergence of the saddle-point formulation is slower than the dual forcing formulation, the increase in computational speed due to time-parallelization can more than compensate for the additional inner-loop iterations required by the saddle-point algorithm in the CCS configuration considered here. Further gains in performance can be achieved by running the 4D-Var inner-loop iterations at reduced resolution and/or reduced arithmetic precision. The results presented here indicate that in high performance computing environments with large numbers of available compute cores, the saddle-point formulation of 4D-Var could significantly reduce the run-time compared to the dual forcing formulation for large data assimilation problems.