Inexpensive Model Research Articles

Insights into the Spin-Lattice Dynamics of Organic Radicals Beyond Molecular Tumbling: A Combined Molecular Dynamics and Machine-Learning Approach

The prediction of spin-lattice dynamics is a challenging computational and theoretical problem due to the complex interplay among atomic motion and spin interactions. Here, we employ machine-learning paradigms to generate a first-principles-accurate and computationally inexpensive model that predicts both conformational energy and spin Hamiltonian parameters of an organic radical as function of its molecular distortions. This model is applied to the study of the g tensor correlation function during molecular dynamics in solution and it is shown that it is possible to access the time dependence of the spin Hamiltonian parameters without making assumptions on the type of molecular motion or spin-lattice dynamics’ time-scales involved. We further use these approach to disentangle inter- and intra-molecular contributions to the g tensor correlation function and provide new insights into the nature of vibronic-coupling in organic semiconductors.

Effect of BMP-2 Adherent to Resorbable Sutures on Cartilage Repair: A Rat Model of Xyphoid Process.

Meniscal tears are often seen in orthopedic practice. The current strategy for meniscal repair has only had limited success with a relatively high incidence of re-operative rate. This study evaluates the therapeutic effects of Bone morphogenetic protein-2 (BMP-2) soaked sutures for cartilage repair, using a rat model of xyphoid healing. Vicryl-resorbable sutures were presoaked in BMP-2 solutions prior to animal experimentation. Rat xyphoid process (an avascular hyaline cartilage structure) was surgically ruptured followed by repair procedures with regular suture or with sutures that were pre-soaked in BMP-2 solutions. In vitro assessment indicated that presoaking the Vicryl-resorbable sutures with 10 µg/mL BMP-2 resulted in a sustained amount of the growth factor release up to 7 days. Histological analysis suggested that application of this BMP-2 soaked suture on the rat xyphoid process model significantly improved the avascular cartilage healing compared to non-soaked control sutures. In conclusion, data here confirm that the rat xyphoid process repair is a reproducible and inexpensive animal model for meniscus and other cartilage repair. More importantly, coating of BMP-2 on sutures appears a potential avenue to improve cartilage repair and regeneration. Further study is warranted to explore the molecular mechanisms of this strategy.

An Overland Flood Model for Geographical Information Systems

A variety of flood models and commercial flood simulation software are provided in the literature, with different accuracies and precisions changing from coarse to fine, depending on model structure and detailed descriptions of basin and hydrologic properties. These models generally focus on river processes, taking overland processes as inputs of 1D or 2D hydrodynamic or hydrologic river flow models. Due to the discrete structure of overland flow and unknown-dynamic boundary conditions, such classical approaches are not cable of fast and reliable spatio–temporal estimations for overland flows, and require detailed and well-organized spatial data that cannot be immediately obtained during an emergency. A spatially-distributed Geographical Information Systems (GIS) based flood model is developed in this study to simulate overland floods, using cellular automata principles. GIS raster cells are considered hydrologic homogeneous areas throughout which hydrologic properties remain constant. Hydrodynamic flow principles, conservations of mass, momentum and energy are applied at pixel level to simulate floodwaters. The proposed GIS model is capable of directly manipulating spatio–temporal pixel level data (e.g., topography, precipitation, infiltration, surface roughness etc.) for modeling of rainfall-induced overland floods; therefore, it can provide fast, temporal and spatial flood depth estimations as well as maximum flood depths and times of concentration for all pixels throughout a study area. The model is quite simple and easy to apply via easily creatable GIS input layers, and is thus very convenient for preliminary engineering applications that need quick and fast response. Its main advantage is that it does not need a predefined flood boundary and boundary conditions. This advantage is especially valuable for coastal plains where delineation of a basin is generally too difficult. Floodwaters of Cyclone Nargis/Myanmar were simulated to test the model. Sensitivity analyses were applied to evaluate the effects of the model parameters (i.e., surface roughness and infiltration rates) on simulation results. The study shows that the proposed GIS model can be readily applied for the fast and inexpensive modeling of rainfall caused floods in areas where flood boundaries and boundary conditions cannot be clearly identified.

Battery Energy Management of Autonomous Electric Vehicles Using Computationally Inexpensive Model Predictive Control

With the emergence of vehicle-communication technologies, many researchers have strongly focused their interest in vehicle energy-efficiency control using this connectivity. For instance, the exploitation of preview traffic enables the vehicle to plan its speed and position trajectories given a prediction horizon so that energy consumption is minimized. To handle the strong uncertainties in the traffic model in the future, a constrained controller is generally employed in the existing researches. However, its expensive computational feature largely prevents its commercialization. This paper addresses computational burden of the constrained controller by proposing a computationally tractable model prediction control (MPC) for real-time implementation in autonomous electric vehicles. We present several remedies to achieve a computationally manageable constrained control, and analyze its real-time computation feasibility and effectiveness in various driving conditions. In particular, both warmstarting and move-blocking methods could relax the computations significantly. Through the validations, we confirm the effectiveness of the proposed approach while maintaining good performance compared to other alternative schemes.

A Murine Model of a Burn Wound Reconstructed with an Allogeneic Skin Graft.

Trivial superficial wounds heal without complications by primary intention. Deep wounds, such as full thickness burns, heal by secondary intention and require surgical debridement and skin grafting. Successful integration of the donor graft into a recipient wound bed depends on timely recruitment of immune cells, robust angiogenic response and new extracellular matrix formation. The development of novel therapeutic agents, which target some key processes involved in wound healing, are hindered by the lack of reliable preclinical models with optimized objective assessment of wound closure. Here, we describe an inexpensive and reproducible model of experimental full thickness burn wound reconstructed with an allogeneic skin graft. The wound is induced on the dorsum surface of anaesthetized inbred wild type mice from the BALB/C and SKH1-Hrhr backgrounds. The burn is produced using a brass template measuring 10 mm in diameter, which is preheated to 80 °C and delivered at a constant pressure for 20 s. Burn eschar is excised 24 hours after the injury and replaced with a full thickness graft harvested from the tail of a genetically similar donor mouse. No specialized equipment is required for the procedure and surgical techniques are straightforward to follow. The method may be effortlessly implemented and reproduced in most research settings. Certain limitations are associated with the model. Due to technical difficulties, the harvest of thinner split thickness skin grafts is not possible. The surgical method we describe here allows for the reconstruction of burn wounds using full thickness skin grafts. It may be used to carry out preclinical therapeutic testing.

Marijuana and Opioid Use during Pregnancy: Using Zebrafish to Gain Understanding of Congenital Anomalies Caused by Drug Exposure during Development.

Marijuana and opioid addictions have increased alarmingly in recent decades, especially in the United States, posing threats to society. When the drug user is a pregnant mother, there is a serious risk to the developing baby. Congenital anomalies are associated with prenatal exposure to marijuana and opioids. Here, we summarize the current data on the prevalence of marijuana and opioid use among the people of the United States, particularly pregnant mothers. We also summarize the current zebrafish studies used to model and understand the effects of these drug exposures during development and to understand the behavioral changes after exposure. Zebrafish experiments recapitulate the drug effects seen in human addicts and the birth defects seen in human babies prenatally exposed to marijuana and opioids. Zebrafish show great potential as an easy and inexpensive model for screening compounds for their ability to mitigate the drug effects, which could lead to new therapeutics.

Lévy walking droplets

L\'evy walks are abnormal random walks, characterized by L\'evy-stable distributed step lengths. L\'evy walks occur in a wide range of phenomena such as foraging, socio-physics. etc. An octanoic acid drop performing a L\'evy walk on aqueous unsaturated octanoic acid solutions is presented as an inanimate, controlled, and inexpensive model system for studying L\'evy walks in a laboratory.

On proper orthogonal decomposition (POD) based reduced-order modeling of groundwater flow through heterogeneous porous media with point source singularity

Groundwater, being a vital component of the natural water resource system, needs continuous monitoring and dynamic management strategies. That said, we require computationally inexpensive groundwater flow models for repetitive solutions with desirable accuracy under budgetary limitation(s). Natural aquifer systems inherit strong heterogeneity at local scales. In this work, we have proposed ordinary kriging-based sequential algorithm for generating replicates of randomly distributed heterogeneous hydraulic conductivity field (Monte Carlo method-based algorithm) conditioned by field values from sampled locations in an irregular-unstructured grid system. Finite Volume method-based groundwater models often encounter difficulties with the representation of point source/sink terms operating within the domain. In this paper, we have proposed an irregular-unstructured grid Finite Volume discretization technique for overcoming the singularity of point source/sink term to yield a consistent output with different grid dimensions. Furthermore, full-system groundwater models often come with a substantial computational burden. Hence, reduction in model order cuts down the computational expenses (in terms of CPU time and usage) to a significant level. We have also put forth a model order reduction methodology for three different illustrative pumping tests. The proposed framework for the model order reduction projects the governing groundwater flow equation onto a set of identified patterns or orthonormal basis functions, applying the Galerkin Projection method to compute a vector of time-dependent coefficients. We have performed pattern identification by Singular Value Decomposition (SVD) of snapshots of full-system model simulation data at selected time instants within the pumping test time domain. The numerical results of the proposed reduced-order models show a good approximation of the full-system models at a comparatively lesser computational time. The accuracy and efficiency of the models attempt to ensure their potential applicability for identifying groundwater dynamics.

Novel Porcine Kidney-Based Microsurgery Training Model for Developing Basic to Advanced Microsurgical Skills.

Microsurgery training is critical to the practice of microvascular procedures in many surgical areas. However, even simple procedures require different levels of complex skills. Therefore, simulation-based surgical training, mainly in the area of vascular anastomosis, is of great importance. In this paper, we present a new microsurgery training model for the development of basic to advanced microsurgical skills. Porcine kidneys were purchased from a legal butchery slaughterhouse. First, kidneys were washed with water to remove blood and clots inside vessels. Then, dissection was performed throughout the vascular pedicle from the renal arteries to the segmentary branches. Finally, the longitudinal sectioning of the kidney parenchyma was performed to expose the vessels necessary for training. Sixty end-to-end anastomoses were performed. Specific instruments and materials were used to perform anastomoses and dissections with magnification by a video system. We evaluated the diameter of vessels, time to perform anastomosis, and patency of anastomosis. There was no great anatomical variation among the porcine kidneys. The total length for dissection training was 25.80 ± 7.44 cm using the arterial and venous vessel. The average time to perform arterial anastomoses was 23.79 ± 4.55 minutes. For vessel diameters of ≤ 3, 4 to 6, and 7 to 10 mm, the average procedure times were 27.68 ± 3.39, 22.92 ± 4.12, and 20.77 ± 3.44 minutes, respectively. Regarding venous anastomosis, the average duration of the procedure was 26.17 ± 4.80 minutes, including durations of 31.61 ± 3.86, 25.66 ± 4.19, and 21.24 ± 3.79 minutes for vessel diameters of ≤ 7, 8 to 10, and >10 mm, respectively. Positive patency was achieved in all surgeries. The porcine kidney provides an inexpensive and convenient biological model for modeling microanastomosis with high fidelity to vascular structures.

Surrogate-assisted Bayesian inversion for landscape and basin evolution models

Abstract. The complex and computationally expensive nature of landscape evolution models poses significant challenges to the inference and optimization of unknown model parameters. Bayesian inference provides a methodology for estimation and uncertainty quantification of unknown model parameters. In our previous work, we developed parallel tempering Bayeslands as a framework for parameter estimation and uncertainty quantification for the Badlands landscape evolution model. Parallel tempering Bayeslands features high-performance computing that can feature dozens of processing cores running in parallel to enhance computational efficiency. Nevertheless, the procedure remains computationally challenging since thousands of samples need to be drawn and evaluated. In large-scale landscape evolution problems, a single model evaluation can take from several minutes to hours and in some instances, even days or weeks. Surrogate-assisted optimization has been used for several computationally expensive engineering problems which motivate its use in optimization and inference of complex geoscientific models. The use of surrogate models can speed up parallel tempering Bayeslands by developing computationally inexpensive models to mimic expensive ones. In this paper, we apply surrogate-assisted parallel tempering where the surrogate mimics a landscape evolution model by estimating the likelihood function from the model. We employ a neural-network-based surrogate model that learns from the history of samples generated. The entire framework is developed in a parallel computing infrastructure to take advantage of parallelism. The results show that the proposed methodology is effective in lowering the computational cost significantly while retaining the quality of model predictions.

Application-oriented mini-plant experiments using non-conventional model foulants to evaluate new hollow fiber membrane materials

Most of literature reporting on performance of ultrafiltration membranes was performed in bench-scale experiments employing flat-sheets at operating conditions irrelevant to full-scale application. Subsequently, there is a critical need for an appropriate lab-scale testing protocol employing reliable fouling surrogates. Common individual foulants, e.g., humic acid, bovine serum albumin and sodium alginate, were extensively reported; however, their ability to resemble organic fouling by real surface waters remains questionable. In this study, potting soil extracts were investigated as reliable and inexpensive model foulants for testing the performance of new modified polyphenylene sulfone (PPSU) hollow fiber membrane modules. Assessment experiments were performed in comparison with corresponding polyethersulfone (PESU) membranes modules using mini-plant testing unit operated at full-scale conditions. At comparable total organic carbon content, aqueous extracts of four different potting soil types had different dissolved organic carbon compositions and turbidity. Humic substances were the main constituents; however, hydrophobic organic carbon (HOC) and biopolymers varied significantly. An application-oriented testing protocol comprising 24 filtration-cycles was developed. Potting soil extract feeds were emphasized to imitate chemical composition and characteristics of moderately organic-loaded surface waters, at high reproducibility, and induce typical organic fouling within experiment time. Feeds exhibiting high biopolymer content (or modest portions of biopolymer and HOC) were able to distinguish explicitly between fouling propensity of different modified membrane materials. Besides regular performance measures, fouling propensity was quantified as hydraulic irreversible fouling index (HIFI) that was related to turbidity removal; however, no consistent correlation was found with humics and low molecular weight organic fractions. Furthermore, impact of feed solution type on the interplay between membranes’ characteristics and HIFI values was investigated. Good correlation between PPSU-based membranes’ characteristics and HIFI values was noticed upon using feeds containing considerable biopolymers and HOC portions. Nevertheless, in case of PESU-based membranes, impact of improvement of pure water permeability (due to modification) was dominating.

Simultaneous Estimation of Vehicle Roll and Sideslip Angles through a Deep Learning Approach.

Presently, autonomous vehicles are on the rise and are expected to be on the roads in the coming years. In this sense, it becomes necessary to have adequate knowledge about its states to design controllers capable of providing adequate performance in all driving scenarios. Sideslip and roll angles are critical parameters in vehicular lateral stability. The later has a high impact on vehicles with an elevated center of gravity, such as trucks, buses, and industrial vehicles, among others, as they are prone to rollover. Due to the high cost of the current sensors used to measure these angles directly, much of the research is focused on estimating them. One of the drawbacks is that vehicles are strong non-linear systems that require specific methods able to tackle this feature. The evolution in Artificial Intelligence models, such as the complex Artificial Neural Network architectures that compose the Deep Learning paradigm, has shown to provide excellent performance for complex and non-linear control problems. In this paper, the authors propose an inexpensive but powerful model based on Deep Learning to estimate the roll and sideslip angles simultaneously in mass production vehicles. The model uses input signals which can be obtained directly from onboard vehicle sensors such as the longitudinal and lateral accelerations, steering angle and roll and yaw rates. The model was trained using hundreds of thousands of data provided by Trucksim® and validated using data captured from real driving maneuvers using a calibrated ground truth device such as VBOX3i dual-antenna GPS from Racelogic®. The use of both Trucksim® software and the VBOX measuring equipment is recognized and widely used in the automotive sector, providing robust data for the research shown in this article.

Decision tree driven construction of rate constant models: Identifying the “top-N” environment atoms that influence surface diffusion barriers in Ag, Cu, Ni, Pd and Pt

The local chemical environment is known to influence the rate constants of thermally activated atomic-scale processes in materials. In situations where rate constants vary over several orders of magnitude, dynamical materials simulations often require accurate rate constant models that can rapidly predict the rate for vast number of environments. Deriving rate constant models by fitting to a database of barriers can be particularly challenging when several environment atoms are believed to affect the rate. Previously, artificial neural networks (ANN) and cluster expansion models (CEM) have been employed as rate constant models. We demonstrate that a decision tree (DT) can complement training of such models by providing useful inputs. DTs can be used to (i) determine the relevant chemical environment, (ii) estimate the accuracy expected from CEM/ANN, (iii) identify cluster sizes required in CEM or size of the input layer in ANN so that the CEM/ANN model can be trained in a single step, and (iv) determine the minimum amount of data required for accurate training. Using this strategy, we construct for the first time CEM and ANN models for the exchange move (surface diffusion of metal on metal) that are both compact and accurate. The use of DT has enabled inclusion of large clusters, as big as 11 atom clusters in the CEM. Our strategy paves way for coupling DT and CEM/ANN for building computationally inexpensive rate constant models.

A Bactrocera oleae (Rossi) damage estimation model to anticipate pest control strategies in olive production

The olive fly, Bactrocera oleae (Rossi), is the main pest in most olive-growing regions. During a 10-year study (2001–2011), olive fly population levels were evaluated in twenty olive groves in the region of Madrid, Spain, as part of the “European Program of Quality Improvement in Olive Oil and Table Olives”. The fly population data obtained by trapping with McPhail traps throughout the season and the damage observed during fruit sampling were analyzed in order to obtain an easy-to-use and inexpensive damage estimation model that could then be used to predict the need for control measures. We observed that the increase in the number of adults caught in McPhail traps was significantly correlated with the increase in production damage. For the same increase in the olive fly population, there was more damage to the olive crop in the years when the date of appearance of the first stung fruit occurred later. Additionally, a significant correlation was obtained between the size of the olive fly population that caused the first damage and the size of the olive fly population that caused the total damage through the end of the harvest season. Therefore, the potential damage to the olive fruit crop at harvest time (usually in December) can be easily estimated in the middle of September by knowing the date that olive fly damage was first detected (first stung date) and by estimating the olive fly population size at the end of the season (obtained empirically from the population size when fruit damage was first detected). This means that prevention and control measures can be anticipated up to three months before the beginning of harvest.

Uncertainty Quantification and Sensitivity Analysis in a Nonlinear Finite-Element Model of a Permanent Magnet Synchronous Machine

The objective of this article is to set forth a computationally efficient methodology to quantify the effects and assess the relevance of geometric and material uncertainty on a permanent magnet synchronous machine (PMSM), based on a nonlinear finite-element model (FEM). Our methodology follows the theory of Gaussian process regression and principal component analysis to build a computationally inexpensive surrogate model that replaces the FEM. Uncertainty quantification and sensitivity analysis studies focus on the electromagnetic torque, flux linkage, and core loss of the PMSM.

A Metamodel-Based Analysis of the Sensitivity and Uncertainty of the Response of Chesapeake Bay Salinity and Circulation to Projected Climate Change

Numerical models are often used to simulate estuarine physics and water quality under scenarios of future climate conditions. However, representing the wide range of uncertainty about future climate often requires an infeasible number of computationally expensive model simulations. Here, we develop and test a computationally inexpensive statistical model, or metamodel, as a surrogate for numerical model simulations. We show that a metamodel fit using only 12 numerical model simulations of Chesapeake Bay can accurately predict the early summer mean salinity, stratification, and circulation simulated by the numerical model given the input sea level, winter–spring streamflow, and tidal amplitude along the shelf. We then use this metamodel to simulate summer salinity and circulation under sampled probability distributions of projected future mean sea level, streamflow, and tidal amplitudes. The simulations from the metamodel show that future salinity, stratification, and circulation are all likely to be higher than present-day averages. We also use the metamodel to quantify how uncertainty about the model inputs transfers to uncertainty in the output and find that the model projections of salinity and stratification are highly sensitive to uncertainty about future tidal amplitudes along the shelf. This study shows that metamodels are a promising approach for robustly estimating the impacts of future climate change on estuaries.

The Gamma-glutamyl Transpeptidase to Platelet Ratio (GPR) Predict Significant Liver Fibrosis and Cirrhosis in Chronic Egyptian HCV Patients

Background and aim: Non- invasive parameters of liver fibrosis are being widely incorporated and adopted in clinical practice, of them, 2 ratios APRI and FIB-4 were proposed and applied. The gamma-glutamyl transferase -to- platelet ratio (GPR) was developed and investigated as available test that is useful in predicting liver fibrosis stages in chronic HBV patients. We aimed to estimate the diagnostic performance of GPR compared to APRI in assessing different fibrosis stages estimated by ultrasound based Transient Elastography in chronic HCV Egyptian patients. Methods: This prospective study was conducted on 90 treatment-naive chronic HCV patients. Fibrosis stages were assessed by Transient Elastography. Serum aspartate transferase, alanine transferase, gamma-glutamyl transferase and platelets were estimated. APRI and GPR formulas were calculated. Results: GPR was significantly different with fibrosis stage (p value F3) from non-significant fibrosis (< F3) was significant with GPR AUC was 0.97 while APRI AUC was 0.86. GPR at cutoff point 0.31 has sensitivity 92 %, specificity 88%, PPV 86 % and NPV 91 %. While, APRI at cutoff 0.26 has sensitivity 81 % and specificity 78 %. Conclusion: The GPR represents a simple, non-invasive, inexpensive model for assessment of liver fibrosis. The GPR is a more accurate model than APRI to stage liver fibrosis in chronic HCV patients in Egypt.

Computer assisted recognition of breast cancer in biopsy images via fusion of nucleus-guided deep convolutional features

Background and objective: Breast cancer is a commonly detected cancer among women, resulting in a high number of cancer-related mortality. Biopsy performed by pathologists is the final confirmation procedure for breast cancer diagnosis. Computer-aided diagnosis systems can support the pathologist for better diagnosis and also in reducing subjective errors.Methods: In the automation of breast cancer analysis, feature extraction is a challenging task due to the structural diversity of the breast tissue images. Here, we propose a nucleus feature extraction methodology using a convolutional neural network (CNN), ‘NucDeep’, for automated breast cancer detection. Non-overlapping nuclei patches detected from the images enable the design of a low complexity CNN for feature extraction. A feature fusion approach with support vector machine classifier (FF + SVM) is used to classify breast tumor images based on the extracted CNN features. The feature fusion method transforms the local nuclei features into a compact image-level feature, thus improving the classifier performance. A patch class probability based decision scheme (NucDeep + SVM + PD) for image-level classification is also introduced in this work.Results: The proposed framework is evaluated on the publicly available BreaKHis dataset by conducting 5 random trials with 70-30 train-test data split, achieving average image level recognition rate of 96.66 ± 0.77%, 100% specificity and 96.21% sensitivity.Conclusion: It was found that the proposed NucDeep + FF + SVM model outperforms several recent existing methods and reveals a comparable state of the art performance even with low training complexity. As an effective and inexpensive model, the classification of biopsy images for breast tumor diagnosis introduced in this research will thus help to develop a reliable support tool for pathologists.

Thermomechanical and geometry model for directed energy deposition with 2D/3D toolpaths

Directed energy deposition (DED) is a metal additive manufacturing process, where dimensional accuracy and repeatability are traditionally challenging to achieve. Strategies for computationally inexpensive process modelling and fast-response process controls of the laser deposition process are necessary to keep the geometric features close to the required dimensional tolerances. The deposition geometry depends highly on the complex local laser-material interaction and global thermal history of the substrate. In order to control the deposition geometry, an accurate and computationally inexpensive discretized state space thermal history model coupled with an analytical deposition geometry model is developed in this work. The model accounts for the local laser-material interaction using the mass and energy equilibrium equations coupled in a lumped parameter solution, as well as the global thermal history of the product using a state space thermomechanical discretization. In literature, studies have only focused on 1D toolpaths with constant process parameters such as speed, powder feedrate, and laser power. As it is possible to achieve highly complex geometric shapes with additive manufacturing, it is important to have models compatible with 2D/3D complex toolpaths. In this paper, an analytical thermomechanical model and a coupled deposition geometry model for DED process are presented and experimentally validated. As such, the thermal history of the deposited part is predicted throughout the process and the geometric features are predicted for 2D toolpaths.

How Biased Is Your Model? Concentration Inequalities, Information and Model Bias

We derive tight and computable bounds on the bias of statistical estimators, or more generally of quantities of interest, when evaluated on a baseline model $P$ rather than on the typically unknown true model $Q$ . Our proposed method combines the scalable information inequality derived by P. Dupuis, K.Chowdhary, the authors and their collaborators together with classical concentration inequalities (such as Bennett’s and Hoeffding-Azuma inequalities). Our bounds are expressed in terms of the Kullback-Leibler divergence $R(Q\|P)$ of model $Q$ with respect to $P$ and the moment generating function for the statistical estimator under $P$ . Furthermore, concentration inequalities, i.e. bounds on moment generating functions, provide tight and computationally inexpensive model bias bounds for quantities of interest. Finally, they allow us to derive rigorous confidence bands for statistical estimators that account for model bias and are valid for an arbitrary amount of data.