Error modelled gene expression analysis (EMOGEA) provides a superior overview of time course RNA-seq measurements and low count gene expression

Temporal RNA-sequencing (RNA-seq) studies of bulk samples provide an opportunity for improved understanding of gene regulation during dynamic phenomena such as development, tumor progression or response to an incremental dose of a pharmacotherapeutic. Moreover, single-cell RNA-seq (scRNA-seq) data implicitly exhibit temporal characteristics because gene expression values recapitulate dynamic processes such as cellular transitions. Unfortunately, temporal RNA-seq data continue to be analyzed by methods that ignore this ordinal structure and yield results that are often difficult to interpret. Here, we present Error Modelled Gene Expression Analysis (EMOGEA), a framework for analyzing RNA-seq data that incorporates measurement uncertainty, while introducing a special formulation for those acquired to monitor dynamic phenomena. This method is specifically suited for RNA-seq studies in which low-count transcripts with small-fold changes lead to significant biological effects. Such transcripts include genes involved in signaling and non-coding RNAs that inherently exhibit low levels of expression. Using simulation studies, we show that this framework down-weights samples that exhibit extreme responses such as batch effects allowing them to be modeled with the rest of the samples and maintain the degrees of freedom originally envisioned for a study. Using temporal experimental data, we demonstrate the framework by extracting a cascade of gene expression waves from a well-designed RNA-seq study of zebrafish embryogenesis and an scRNA-seq study of mouse pre-implantation and provide unique biological insights into the regulation of genes in each wave. For non-ordinal measurements, we show that EMOGEA has a much higher rate of true positive calls and a vanishingly small rate of false negative discoveries compared to common approaches. Finally, we provide two packages in Python and R that are self-contained and easy to use, including test data.

Overall Profile Measurements of Tiny Parts with Complicated Features with the Cradle-Type Five-Axis System

There are generally complex features with large curvature or narrow space on surfaces of complicated tiny parts, which makes high-precision measurements of their three-dimensional (3D) overall profiles a long-lasting industrial problem. This paper proposes a feasible measurement solution to this problem, by designing a cradle-type point-scanning five-axis measurement system. All the key technology of this system is also studied from the system construction to the actual measurement process, and the measurement accuracy is improved through error calibration and compensation. Finally, the feasibility is proved by engineering realization. The measurement capability of the system is verified by measuring workpieces such as cross cylinders and microtriangular pyramids.

Using First Principles for Deep Learning and Model-Based Control of Soft Robots

Model-based optimal control of soft robots may enable compliant, underdamped platforms to operate in a repeatable fashion and effectively accomplish tasks that are otherwise impossible for soft robots. Unfortunately, developing accurate analytical dynamic models for soft robots is time-consuming, difficult, and error-prone. Deep learning presents an alternative modeling approach that only requires a time history of system inputs and system states, which can be easily measured or estimated. However, fully relying on empirical or learned models involves collecting large amounts of representative data from a soft robot in order to model the complex state space–a task which may not be feasible in many situations. Furthermore, the exclusive use of empirical models for model-based control can be dangerous if the model does not generalize well. To address these challenges, we propose a hybrid modeling approach that combines machine learning methods with an existing first-principles model in order to improve overall performance for a sampling-based non-linear model predictive controller. We validate this approach on a soft robot platform and demonstrate that performance improves by 52% on average when employing the combined model.

SAD phasing of XFEL data depends critically on the error model

A nonlinear least-squares method for refining a parametric expression describing the estimated errors of reflection intensities in serial crystallographic (SX) data is presented. This approach, which is similar to that used in the rotation method of crystallographic data collection at synchrotrons, propagates error estimates from photon-counting statistics to the merged data. Here, it is demonstrated that the application of this approach to SX data provides better SAD phasing ability, enabling the autobuilding of a protein structure that had previously failed to be built. Estimating the error in the merged reflection intensities requires the understanding and propagation of all of the sources of error arising from the measurements. One type of error, which is well understood, is the counting error introduced when the detector counts X-ray photons. Thus, if other types of random errors (such as readout noise) as well as uncertainties in systematic corrections (such as from X-ray attenuation) are completely understood, they can be propagated along with the counting error, as appropriate. In practice, most software packages propagate as much error as they know how to model and then include error-adjustment terms that scale the error estimates until they explain the variance among the measurements. If this is performed carefully, then during SAD phasing likelihood-based approaches can make optimal use of these error estimates, increasing the chance of a successful structure solution. In serial crystallography, SAD phasing has remained challenging, with the few examples of de novo protein structure solution each requiring many thousands of diffraction patterns. Here, the effects of different methods of treating the error estimates are estimated and it is shown that using a parametric approach that includes terms proportional to the known experimental uncertainty, the reflection intensity and the squared reflection intensity to improve the error estimates can allow SAD phasing even from weak zinc anomalous signal.

Conservative Sensor Error Modeling Using a Modified Paired Overbound Method and its Application in Satellite-Based Augmentation Systems

Conservative sensor error modeling is of great significance in the field of safety-of-life. At present, the overbound method has been widely used in areas such as satellite-based augmentation systems (SBASs) and ground-based augmentation systems (GBASs) that provide integrity service. It can effectively solve the difficulties of non-Gaussian and non-zero mean error modeling and confidence interval estimation of user position error. However, there is still a problem in that the model is too conservative and leads to the lack of availability. In order to further improve the availability of SBASs, an improved paired overbound method is proposed in this paper. Compared with the traditional method, the improved algorithm no longer requires the overbound function to conform to the characteristics of the probability distribution function, so that under the premise of ensuring the integrity of the system, the real error characteristics can be more accurately modeled and measured. The experimental results show that the modified paired overbound method can improve the availability of the system with a probability of about 99%. In view of the fact that conservative error modeling is more sensitive to large deviations, this paper analyzes the robustness of the improved algorithm in the case of abnormal data loss. The maximum deviation under a certain integrity risk is used to illustrate the effectiveness of the improved paired overbound method compared with the original method.

Modeling the Influence of Oil Film, Position and Orientation Parameters on the Accuracy of a Laser Triangulation Probe

The laser triangulation probe conveniently obtains surface topography data of a measured target. However, compared to the touch probe, its reliability and accuracy can be negatively affected by various factors associated with the object being measured and the probe itself. In this paper, to identify potential compensation strategies to improve the accuracy of depth measurement for laser triangulation probe, the measuring errors caused by an oil film on the measured surface, and the probe’s position and orientation parameters with respect to the measuring object (including scan depth, incident angle, and azimuth angle), were studied. A theoretical model based on the geometrical optics, and an empirical model from the error evaluations, were established to quantitatively characterize the error influence of oil film and probe’s parameters, respectively. We also investigated the influence pattern of different filtering methods with several comparison experiments. The verification procedures, measuring both a free-form surface (chevron-corrugated plate) and a gauge block covered with an oil film, demonstrate that these models and measurement suggestions are viable methods for predicting theoretical error and can be used as compensation references to improve the accuracy of depth measurement to the laser triangulation probe.

A Separated Calibration Method for Inertial Measurement Units Mounted on Three-Axis Turntables

Inertial Measurement Unit (IMU) calibration accuracy is easily affected by turntable errors, so the primary aim of this study is to reduce the dependence on the turntable’s precision during the calibration process. Firstly, the indicated-output of the IMU considering turntable errors is constructed and with the introduction of turntable errors, the functional relationship between turntable errors and the indicated-output was derived. Then, based on a D-suboptimal design, a calibration method for simultaneously identifying the IMU error model parameters and the turntable errors was proposed. Simulation results showed that some turntable errors could thus be effectively calibrated and automatically compensated. Finally, the theoretical validity was verified through experiments. Compared with the traditional method, the method proposed in this paper can significantly reduce the influence of the turntable errors on the IMU calibration accuracy.

QUADRATIC: Quality of Dice in Registration Circuits

Image registration involves identification of a transformation to fit a target image to a reference image space. The success of the registration process is vital for correct interpretation of the results of many medical image-processing applications, including multi-atlas segmentation. While there are several validation metrics employed in rigid registration to examine the accuracy of the method, non-rigid registrations (NRR) are validated subjectively in most cases, validated in offline cases, or based on image similarity metrics, all of which have been shown to poorly correlate with true registration quality. In this paper, we model the error for each target scan by expanding on the idea of Assessing Quality Using Image Registration Circuits (AQUIRC), which created a model for error "quality" associated with NRR. In this paper, we model the Dice similarity coefficient (DSC) error in the network, for a more interpretable measure. We test four functional models using a leave-one-out strategy to evaluate the relationship between edge DSC and circuit DSC: linear, quadratic, third order, or multiplicative models. We found that the quadratic model most accurately learns the NRR-DSC, with a median correlation coefficient of 0.58 with the true NRR-DSC, we call this the QUADRATIC (QUAlity of Dice in RegistrATIon Circuits) model. The QUADRATIC model is used for multi-atlas segmentation based on majority vote. Choosing the four best atlases predicted from the QUDRATIC model resulted in a 7% increase in the DSC between segmented image and true labels.

Error Modeling and Experimental Study of a Flexible Joint 6-UPUR Parallel Six-Axis Force Sensor

By combining a parallel mechanism with integrated flexible joints, a large measurement range and high accuracy sensor is realized. However, the main errors of the sensor involve not only assembly errors, but also deformation errors of its flexible leg. Based on a flexible joint 6-UPUR (a kind of mechanism configuration where U-universal joint, P-prismatic joint, R-revolute joint) parallel six-axis force sensor developed during the prephase, assembly and deformation error modeling and analysis of the resulting sensors with a large measurement range and high accuracy are made in this paper. First, an assembly error model is established based on the imaginary kinematic joint method and the Denavit-Hartenberg (D-H) method. Next, a stiffness model is built to solve the stiffness matrix. The deformation error model of the sensor is obtained. Then, the first order kinematic influence coefficient matrix when the synthetic error is taken into account is solved. Finally, measurement and calibration experiments of the sensor composed of the hardware and software system are performed. Forced deformation of the force-measuring platform is detected by using laser interferometry and analyzed to verify the correctness of the synthetic error model. In addition, the first order kinematic influence coefficient matrix in actual circumstances is calculated. By comparing the condition numbers and square norms of the coefficient matrices, the conclusion is drawn theoretically that it is very important to take into account the synthetic error for design stage of the sensor and helpful to improve performance of the sensor in order to meet needs of actual working environments.

Depth Errors Analysis and Correction for Time-of-Flight (ToF) Cameras

Time-of-Flight (ToF) cameras, a technology which has developed rapidly in recent years, are 3D imaging sensors providing a depth image as well as an amplitude image with a high frame rate. As a ToF camera is limited by the imaging conditions and external environment, its captured data are always subject to certain errors. This paper analyzes the influence of typical external distractions including material, color, distance, lighting, etc. on the depth error of ToF cameras. Our experiments indicated that factors such as lighting, color, material, and distance could cause different influences on the depth error of ToF cameras. However, since the forms of errors are uncertain, it’s difficult to summarize them in a unified law. To further improve the measurement accuracy, this paper proposes an error correction method based on Particle Filter-Support Vector Machine (PF-SVM). Moreover, the experiment results showed that this method can effectively reduce the depth error of ToF cameras to 4.6 mm within its full measurement range (0.5–5 m).

Increasing Safety of a Robotic System for Inner Ear Surgery Using Probabilistic Error Modeling Near Vital Anatomy

Safe and effective planning for robotic surgery that involves cutting or ablation of tissue must consider all potential sources of error when determining how close the tool may come to vital anatomy. A pre-operative plan that does not adequately consider potential deviations from ideal system behavior may lead to patient injury. Conversely, a plan that is overly conservative may result in ineffective or incomplete performance of the task. Thus, enforcing simple, uniform-thickness safety margins around vital anatomy is insufficient in the presence of spatially varying, anisotropic error. Prior work has used registration error to determine a variable-thickness safety margin around vital structures that must be approached during mastoidectomy but ultimately preserved. In this paper, these methods are extended to incorporate image distortion and physical robot errors, including kinematic errors and deflections of the robot. These additional sources of error are discussed and stochastic models for a bone-attached robot for otologic surgery are developed. An algorithm for generating appropriate safety margins based on a desired probability of preserving the underlying anatomical structure is presented. Simulations are performed on a CT scan of a cadaver head and safety margins are calculated around several critical structures for planning of a robotic mastoidectomy.

A comparison between different error modeling of MEMS applied to GPS/INS integrated systems

Advances in the development of micro-electromechanical systems (MEMS) have made possible the fabrication of cheap and small dimension accelerometers and gyroscopes, which are being used in many applications where the global positioning system (GPS) and the inertial navigation system (INS) integration is carried out, i.e., identifying track defects, terrestrial and pedestrian navigation, unmanned aerial vehicles (UAVs), stabilization of many platforms, etc. Although these MEMS sensors are low-cost, they present different errors, which degrade the accuracy of the navigation systems in a short period of time. Therefore, a suitable modeling of these errors is necessary in order to minimize them and, consequently, improve the system performance. In this work, the most used techniques currently to analyze the stochastic errors that affect these sensors are shown and compared: we examine in detail the autocorrelation, the Allan variance (AV) and the power spectral density (PSD) techniques. Subsequently, an analysis and modeling of the inertial sensors, which combines autoregressive (AR) filters and wavelet de-noising, is also achieved. Since a low-cost INS (MEMS grade) presents error sources with short-term (high-frequency) and long-term (low-frequency) components, we introduce a method that compensates for these error terms by doing a complete analysis of Allan variance, wavelet de-nosing and the selection of the level of decomposition for a suitable combination between these techniques. Eventually, in order to assess the stochastic models obtained with these techniques, the Extended Kalman Filter (EKF) of a loosely-coupled GPS/INS integration strategy is augmented with different states. Results show a comparison between the proposed method and the traditional sensor error models under GPS signal blockages using real data collected in urban roadways.

Error modeling and calibration for encoded sun sensors

Error factors in the encoded sun sensor (ESS) are analyzed and simulated. Based on the analysis results, an ESS error compensation model containing structural errors and fine-code algorithm errors is established, and the corresponding calibration method for model parameters is proposed. As external parameters, installation deviation between ESS and calibration equipment are introduced to the ESS calibration model, so that the model parameters can be calibrated accurately. The experimental results show that within plus/minus 60 degree of incident angle, the ESS measurement accuracy after compensation is three times higher on average than that before compensation.