Optimization of a deep mutational scanning workflow to improve quantification of mutation effects on protein-protein interactions.

Deep Mutational Scanning (DMS) assays are powerful tools to study sequence-function relationships by measuring the effects of thousands of sequence variants on protein function. During a DMS experiment, several technical artefacts might distort non-linearly the functional score obtained, potentially biasing the interpretation of the results. We therefore tested several technical parameters in the deepPCA workflow, a DMS assay for protein-protein interactions, in order to identify technical sources of non-linearities. We found that parameters common to many DMS assays such as amount of transformed DNA, timepoint of harvest and library composition can cause non-linearities in the data. Designing experiments in a way to minimize these non-linear effects will improve the quantification and interpretation of mutation effects.

Minimizing electric fields and increasing peripheral nerve stimulation thresholds using a body gradient array coil.

PURPOSE: To demonstrate the performance of gradient array coils in minimizing switched-gradient-induced electric fields (E-fields) and improving peripheral nerve stimulation (PNS) thresholds while generating gradient fields with adjustable linearity across customizable regions of linearity (ROLs). METHODS: A body gradient array coil is used to reduce the induced E-fields on the surface of a body model by modulating applied currents. This is achieved by performing an optimization problem with the peak E-field as the objective function and current amplitudes as unknown variables. Coil dimensions and winding patterns are fixed throughout the optimization, whereas other engineering metrics remain adjustable. Various scenarios are explored by manipulating adjustable parameters. RESULTS: The array design consistently yields lower E-fields and higher PNS thresholds across all scenarios compared with a conventional coil. When the gradient array coil generates target gradient fields within a 44-cm-diameter spherical ROL, the maximum E-field is reduced by 10%, 18%, and 61% for the X, Y, and Z gradients, respectively. Transitioning to a smaller ROL (24 cm) and relaxing the gradient linearity error results in further E-field reductions. In oblique gradients, the array coil demonstrates the most substantial reduction of 40% in the Z-Y direction. Among the investigated scenarios, the most significant increase of 4.3-fold is observed in the PNS thresholds. CONCLUSION: Our study demonstrated that gradient array coils offer a promising pathway toward achieving high-performance gradient coils regarding gradient strength, slew rate, and PNS thresholds, especially in scenarios in which linear magnetic fields are required within specific target regions.

Linearity assessment: deviation from linearity and residual of linear regression approaches.

In this computer simulation study, we examine four different statistical approaches of linearity assessment, including two variants of deviation from linearity (individual (IDL) and averaged (AD)), along with detection capabilities of residuals of linear regression (individual and averaged). From the results of the simulation, the following broad suggestions are provided to laboratory practitioners when performing linearity assessment. A high imprecision can challenge linearity investigations by producing a high false positive rate or low power of detection. Therefore, the imprecision of the measurement procedure should be considered when interpreting linearity assessment results. In the presence of high imprecision, the results of linearity assessment should be interpreted with caution. Different linearity assessment approaches examined in this study performed well under different analytical scenarios. For optimal outcomes, a considered and tailored study design should be implemented. With the exception of specific scenarios, both ADL and IDL methods were suboptimal for the assessment of linearity compared. When imprecision is low (3 %), averaged residual of linear regression with triplicate measurements and a non-linearity acceptance limit of 5 % produces <5 % false positive rates and a high power for detection of non-linearity of >70 % across different types and degrees of non-linearity. Detection of departures from linearity are difficult to identify in practice and enhanced methods of detection need development.

Fibrous Conductive Metallogels with Hybrid Electron/Ion Networks for Boosted Extreme Sensitivity and High Linearity Strain Sensor.

Fibrous strain sensing materials with both high sensitivity and high linearity are of significant importance for wearable sensors, yet they still face great challenges. Herein, a photo-spun reaction encapsulation strategy is proposed for the continuous fabrication of fibrous strain sensor materials (AMGF) with a core-sheath structure. Metallogels (MOGs) formed by bacterial cellulose (BC) nanofibers and Ag nanoparticles (AgNPs), and thermoplastic elastomers (TPE) are employed as the core and sheath, respectively. The in situ ultraviolet light reduction of Ag+ ensured AgNPs to maintain the interconnections between the BC nanofibers and form electron conductive networks (0.31 S m-1 ). Under applied strain, the BC nanofibers experience separation, bringing AMGF a high sensitivity (gauge factor 4.36). The concentration of free ions in the MOGs uniformly varies with applied deformation, endowing AMGF with high linearity and a goodness-of-fit of 0.98. The sheath TPE provided AMGF sensor with stable working life (>10 000 s). Furthermore, the AMGF sensors are demonstrated to monitor complex deformations of the dummy joints in real-time as a wearable sensor. Therefore, the fibrous hybrid conductive network fibers fabricated via the photo-spun reaction encapsulation strategy provide a new route for addressing the challenge of achieving both high sensitivity and high linearity.

Long-term noise exposures and cardiovascular diseases mortality: A study in 5 U.S. states.

BACKGROUND: Previous studies have linked noise exposure with adverse cardiovascular events. However, evidence remains inconsistent, and most previous studies only focused on traffic noise, excluding other anthropogenic sources like constructions, industrial process and commercial activities. Additionally, few studies have been conducted in the U.S. or evaluated the non-linear exposure-response relationships. METHODS: We conducted a relative incidence analysis study using all cardiovascular diseases mortality as cases (n = 936,019) and external causes mortality (n = 232,491) as contrast outcomes. Mortality records geocoded at residential addresses were obtained from five U.S. states (Indiana, 2007; Kansas, 2007-2009, Missouri, 2010-2019, Ohio, 2007-2013, Texas, 2007-2016). Time-invariant long-term noise exposure was obtained from a validated model developed based on acoustical measurements across 2000-2014. Noises from both natural sources (natural activities, including animals, insects, winds, water flows, thunder, etc.) and anthropogenic sources (human activities, including transportation, industrial activities, community facilities & infrastructures, commercial activities, entertainments, etc.) were included. We used daytime and nighttime total anthropogenic noise & day-night average sound pressure level combining natural and anthropogenic sources as exposures. Logistic regression models were fit controlling for Census tract-level & individual-level characteristics. We examined potential modification by sex by interaction terms and potential non-linear associations by thin plate spline terms. RESULTS: We observed positive associations for daytime anthropogenic L50 (sound level exceeded 50% of time) noise (10-dBA OR = 1.047, 95%CI 1.025-1.069), nighttime anthropogenic L50 noise (10-dBA OR = 1.061, 95%CI 1.033-1.091) in a two-exposure-term model, and overall Ldn (day-night average) sound pressure level (10-dBA OR = 1.064, 95%CI 1.040-1.089) in single-exposure-term model. Females were more susceptible to all three exposures. All exposures showed monotonic positive associations with cardiovascular mortality up to certain thresholds around 45-55 dBA, with a generally flattened or decreasing trend beyond those thresholds. CONCLUSIONS: Both daytime anthropogenic and nighttime anthropogenic noises were associated with cardiovascular disease mortality, and associations were stronger in females.

More Than the Sum of Its Parts: Visual-Tactile Integration in the Behaving Rat.

We experience the world by constantly integrating cues from multiple modalities to form unified sensory percepts. Once familiar with multimodal properties of an object, we can recognize it regardless of the modality involved. In this chapter we will examine the case of a visual-tactile orientation categorization experiment in rats. We will explore the involvement of the cerebral cortex in recognizing objects through multiple sensory modalities. In the orientation categorization task, rats learned to examine and judge the orientation of a raised, black and white grating using touch, vision, or both. Their multisensory performance was better than the predictions of linear models for cue combination, indicating synergy between the two sensory channels. Neural recordings made from a candidate associative cortical area, the posterior parietal cortex (PPC), reflected the principal neuronal correlates of the behavioral results: PPC neurons encoded both graded information about the object and categorical information about the animal's decision. Intriguingly single neurons showed identical responses under each of the three modality conditions providing a substrate for a neural circuit in the cortex that is involved in modality-invariant processing of objects.

Usability of sand samples in TL Radiation Dosimetry.

This study investigated natural sand thermoluminescence (TL) response as a possible option for retrospective high-dose gamma dosimetry. The natural sand under investigation was collected from six locations with selection criteria for sampling sites covering the highest probability of exposure to unexpected radiation on the Egyptian coast. Dose-response, glow curve, chemical composition, linearity, and fading rate for different sand samples were studied. Energy Dispersive X-ray Spectroscopy (EDX) analysis revealed differences in chemical composition among the various geological sites, leading to variations in TL glow curve intensity. Sand samples collected from Ras Sedr, Taba, Suez, and Enshas showed similar TL patterns, although with different TL intensities. Beach sands of Matrouh and North Coastal with a high calcite content did not show a clear linear response to the TL technique, in the dose range of 10 Gy up to 30 kGy. The results show that most sand samples are suitable as a radiation dosimeter at accidental levels of exposure. It is proposed here that for high-dose gamma dosimetry with doses ranging from 3 to 10 kGy, a single calibration factor might be enough for TL measurements using sand samples. However, proper calibration might allow dose assessment for doses even up to 30 kGy. Most of the investigated sand samples had nearly stable fading rates after seven days of storage. The Ras Sedr sands sample was the most reliable for retrospective dose reconstruction.

From a glimpse into the key aspects of calibration and correlation to their practical considerations in chemical analysis.

In this tutorial review, we provide a guiding reference on the good practice in building calibration and correlation experiments, and we explain how the results should be evaluated and interpreted. The review centers on calibration experiments where the relationship between response and concentration is expected to be linear, although certain of the described principles of good practice can be applied to non-linear systems, as well. Furthermore, it gives prominence to the meaning and correct interpretation of some of the statistical terms commonly associated with calibration and regression. To reach a mutual understanding in this significant field, we present, through a practical example, a step-by-step procedure, which deals with typical challenges related to linearity and outlier assessment, calculation of the associated error of the predicted concentration, and limits of detection. The utilization of regression lines to compare analytical methods is also elaborated. The results of regression and correlation data are acquired by implementing the Excel spreadsheet of Microsoft, being perhaps one of the most widely used user-friendly software in education and research.

Enhancing Linearity of Light Response in Avalanche Photodiodes by Suppressing Electrode Size Effect.

The nonlinear characteristics of avalanche photodiodes (APDs) inhibit their performance in high-speed communication systems, thereby limiting their widespread application as optical detectors. Existing theoretical models have not fully elucidated complex phenomena encountered in actual device structures. In this study, actual APD structures exhibiting lower linearity than their ideal counterparts were revealed. Simulation analysis and physical inference based on GaN APDs reveal that electrode size is a noteworthy factor influencing response linearity. This discovery expands the nonlinear theory of APDs, suggesting that APD linearity can be enhanced by suppressing the electrode size effect. A physical model was developed to explain this phenomenon, which is attributed to charge accumulation at the edge of the contact layer. Therefore, we proposed an improved APD design that incorporates an additional gap layer and a buffer layer to stabilize the internal gain under high-current-density conditions, thereby enhancing linearity. Our improved APD design increases the linear threshold for optical input power by 4.46 times. This study not only refines the theoretical model for APD linearity but also opens new pathways for improving the linearity of high-speed optoelectronic detectors.

Correcting the Non-Linear Response of Silicon Photomultipliers.

The finite number of pixels in a silicon photomultiplier (SiPM) limits its dynamic range to light pulses up to typically 80% of the total number of pixels in a device. Correcting the non-linear response is essential to extend the SiPM's dynamic range. One challenge in determining the non-linear response correction is providing a reference linear light source. Instead, the single-step method used to calibrate PMTs is applied, based on the difference in responses to two light sources. With this method, the response of an HPK SiPM (S14160-1315PS) is corrected to linearity within 5% while extending the linear dynamic range by a factor larger than ten. The study shows that the response function does not vary by more than 5% for a variation in the operating voltage between 2 and 5 V overvoltage in the gate length between 20 and 100 ns and for a time delay between the primary and secondary light of up to 40 ns.

Design of Fluxgate Current Sensor Based on Magnetization Residence Times and Neural Networks.

This study introduces a novel fluxgate current sensor with a compact, ring-shaped configuration that exhibits improved performance through the integration of magnetization residence times and neural networks. The sensor distinguishes itself with a unique magnetization profile, denoted as M waves, which emerge from the interaction between the target signal and ambient magnetic interference, effectively enhancing interference suppression. These M waves highlight the non-linear coupling between the magnetic field and magnetization residence times. Detection of these residence times is accomplished using full-wave rectification circuits and a Schmitt trigger, with a digital output provided by timing sequence detection. A dual-layer feedforward neural network deciphers the target signal, exploiting this non-linear relationship. The sensor achieves a linearity error of 0.054% within a measurement range of 15 A. When juxtaposed with conventional sensors utilizing the residence-time difference strategy, our sensor reduces linearity error by more than 40-fold and extends the effective measurement range by 150%. Furthermore, it demonstrates a significant decrease in ambient magnetic interference.

A Piezoelectric-Piezoresistive Coupling Electric Field Sensor for Large Dynamic Range AC Electric Field Measurements.

We propose a piezoelectric-piezoresistive coupling electric field sensor capable of performing large dynamic range AC electric field measurements. The electric field sensor utilizes direct coupling between piezoelectric (PE) materials and piezoresistive (PR) strain gauges, in conjunction with an external signal conditioning circuit, to measure AC electric fields effectively. We verified the feasibility of the scheme using a finite element simulation, fabricated a prototype of the electric field sensor, and characterized the properties of the prototype. The testing results indicate that the sensor exhibits an ac resolution of 50 V/m and a linear measurable electric field range of 0 to over 200 kV/m, which keeps the linearity at less than 0.94% from 1 Hz to over 5 kHz. Furthermore, the sensor also has advantages, such as a small size and low power consumption. The sensor can enhance the comprehensive observability and measurability of digital power grids.

Metrology of Short-Length Measurers-Development of a Comparator for the Calibration of Measurers Based on Image Processing and Interferometric Measurements.

For the calibration of linear scales, comparators are generally used. Comparators are devices that enable the movement of an evaluation apparatus over a calibrated scale along a linear base with high precision. The construction of a comparator includes a movable carriage that carries the device for the evaluation of the position of the given edge of the line scale relative to the beginning of the scale. In principle, it involves a camera capturing the scale of the measurer, where the position of the camera's projection center is measured using an interferometer. This article addresses the development of a comparator assembled from low-cost components, as well as the description of systematic influences related to the movement of individual parts of the system, such as the inclination and rotation of the camera and directional and height deviations during the carriage's movement. This article also includes an evaluation of the edge of the given scale with subpixel accuracy, addressing distortion elimination and excluding the influences of impurities or imperfections on the scale. The proposed solution was applied to linear-scale measurers, such as leveling rods with coded and conventional scales and measuring tapes. The entire process of measurement and evaluation was automated.

IoT-Based Heartbeat Rate-Monitoring Device Powered by Harvested Kinetic Energy.

Remote patient-monitoring systems are helpful since they can provide timely and effective healthcare facilities. Such online telemedicine is usually achieved with the help of sophisticated and advanced wearable sensor technologies. The modern type of wearable connected devices enable the monitoring of vital sign parameters such as: heart rate variability (HRV) also known as electrocardiogram (ECG), blood pressure (BLP), Respiratory rate and body temperature, blood pressure (BLP), respiratory rate, and body temperature. The ubiquitous problem of wearable devices is their power demand for signal transmission; such devices require frequent battery charging, which causes serious limitations to the continuous monitoring of vital data. To overcome this, the current study provides a primary report on collecting kinetic energy from daily human activities for monitoring vital human signs. The harvested energy is used to sustain the battery autonomy of wearable devices, which allows for a longer monitoring time of vital data. This study proposes a novel type of stress- or exercise-monitoring ECG device based on a microcontroller (PIC18F4550) and a Wi-Fi device (ESP8266), which is cost-effective and enables real-time monitoring of heart rate in the cloud during normal daily activities. In order to achieve both portability and maximum power, the harvester has a small structure and low friction. Neodymium magnets were chosen for their high magnetic strength, versatility, and compact size. Due to the non-linear magnetic force interaction of the magnets, the non-linear part of the dynamic equation has an inverse quadratic form. Electromechanical damping is considered in this study, and the quadratic non-linearity is approximated using MacLaurin expansion, which enables us to find the law of motion for general case studies using classical methods for dynamic equations and the suitable parameters for the harvester. The oscillations are enabled by applying an initial force, and there is a loss of energy due to the electromechanical damping. A typical numerical application is computed with Matlab 2015 software, and an ODE45 solver is used to verify the accuracy of the method.

A Self-Rectifying Synaptic Memristor Array with Ultrahigh Weight Potentiation Linearity for a Self-Organizing-Map Neural Network.

Two-terminal self-rectifying (SR)-synaptic memristors are preeminent candidates for high-density and efficient neuromorphic computing, especially for future three-dimensional integrated systems, which can self-suppress the sneak path current in crossbar arrays. However, SR-synaptic memristors face the critical challenges of nonlinear weight potentiation and steep depression, hindering their application in conventional artificial neural networks (ANNs). Here, a SR-synaptic memristor (Pt/NiOx/WO3-x:Ti/W) and cross-point array with sneak path current suppression features and ultrahigh-weight potentiation linearity up to 0.9997 are introduced. The image contrast enhancement and background filtering are demonstrated on the basis of the device array. Moreover, an unsupervised self-organizing map (SOM) neural network is first developed for orientation recognition with high recognition accuracy (0.98) and training efficiency and high resilience toward both noises and steep synaptic depression. These results solve the challenges of SR memristors in the conventional ANN, extending the possibilities of large-scale oxide SR-synaptic arrays for high-density, efficient, and accurate neuromorphic computing.

[Erratum in "Point-of-Care Blood Glucose Testing: Post-Market Performance Assessment of the Accu-Chek Inform II Hospital-Use Glucose Meter" (DOI: 10.26442/00403660.2023.12.202522)].

In the article "Point-of-care blood glucose testing: post-market performance assessment of the Accu-Chek Inform II hospital-use glucose meter," published in the Terapevticheskii Arkhiv journal, Vol. 95, No.12, 2023 (DOI: 10.26442/00403660.2023.12.202522), errors were made: the term "measurements at the place of treatment" was changed, as well as the section "Conflict of interest." At the request of the authors' team, errors in the conflict of interest and the wording of the term have been corrected, and the section "Information about the authors" has been updated. The publisher replaced the original version of the published article with the corrected one; the information on the website was also corrected. Correct text of the section "Conflict of interest": Conflict of interest. All authors are not employees or consultants of Roche Diagnostics and have not received any compensation from Roche Diagnostics. Correct wording of the term in Russian: "измерения по месту лечения". Changes were made to the title of the article in Russian: "Измерения глюкозы по месту лечения: пострегистрационное испытание госпитального глюкометра Акку-Чек Информ II", the text of the abstract, keywords, citation, in the text of the article, and abbreviations. Information of the place of work has been updated: Center for Laboratory Diagnostics of the Russian Children Clinical Hospital, a Branch of the Pirogov Russian National Research Medical University. The publisher apologizes to readers and authors for the errors and is confident that the correction of errors will ensure the correct perception and interpretation of the results of the study described in the text.

The N-terminal domain of the Agrobacterium tumefaciens telomere resolvase, TelA, regulates its DNA cleavage and rejoining activities.

Linear replicons can be found in a minority of prokaryotic organisms, including Borrelia species and Agrobacterium tumefaciens. The problem with replicating the lagging strand end of linear DNAs is circumvented in these organisms by the presence of covalently closed DNA hairpin telomeres at the DNA termini. Telomere resolvases are enzymes responsible for generating these hairpin telomeres from a dimeric replication intermediate through a two-step DNA cleavage and rejoining reaction referred to as telomere resolution. It was previously shown that the agrobacterial telomere resolvase, TelA, possesses ssDNA annealing activity in addition to telomere resolution activity. The annealing activity derives, chiefly, from the N-terminal domain. This domain is dispensable for telomere resolution. In this study, we used activity analyses of an N-terminal domain deletion mutant, domain add back experiments, and protein-protein interaction studies and we report that the N-terminal domain of TelA is involved in inhibitory interactions with the remainder of TelA that are relieved by the binding of divalent metal ions. We also found that the regulation of telomere resolution by the N-terminal domain of TelA extends to suppression of inappropriate enzymatic activity, including hairpin telomere fusion (reaction reversal) and recombination between replicated telomeres to form a Holliday junction.

Nonlinear relationship between atherogenic index of plasma and the risk of prediabetes: a retrospective study based on Chinese adults.

BACKGROUND: The atherogenic index of plasma (AIP) can reflect the burden of atherosclerosis. Hyperglycemia is one of the leading causes of atherosclerosis. However, the relationship between AIP and prediabetes is rarely studied. Therefore, we aimed to explore the relationship between AIP and prediabetes. METHODS: This retrospective cohort study recruited 100,069 Chinese adults at the Rich Healthcare Group from 2010 to 2016. AIP was calculated according to Log10 (triglyceride/high-density lipoprotein cholesterol) formula. Cox regression method, sensitivity analyses and subgroup analyses were used to examine the relationship between AIP and prediabetes. Cox proportional hazards regression with cubic spline functions and smooth curve fitting was performed to explore the non-linearity between AIP and prediabetes. The two-piece Cox proportional hazards regression model was used to determine the inflection point of AIP on the risk of prediabetes. RESULTS: After adjusting for confounding covariates, AIP was positively associated with prediabetes (HR: 1.41, 95%CI: 1.31-1.52, P < 0.0001). The two-piecewise Cox proportional hazards regression model discovered that the AIP's inflection point was 0.03 (P for log-likelihood ratio test < 0.001). AIP was positively associated with the risk of prediabetes when AIP ≤ 0.03 (HR: 1.90, 95%CI: 1.66-2.16, P < 0.0001). In contrast, When AIP > 0.03, their association was not significant (HR: 1.04, 95%CI: 0.91-1.19, P = 0.5528). CONCLUSION: This study shows that AIP was positively and non-linearly associated with the risk of prediabetes after adjusting for other confounding factors. When AIP ≤ 0.03, AIP was positively associated with the risk of prediabetes.

Determinative Effect of Axial Linearity on Single-Molecule Magnet Performance in Dinuclear Dysprosium Complexes.

Two dichloride-bridged dinuclear dysprosium(III) complexes based on salen ligands, namely, [Dy(L1 )(µ-Cl)(thf)]2 (1; H2 L1 =N,N'-bis(3,5-di-tert-butylsalicylidene)phenylenediamine) and [Dy2 (L2 )2 (µ-Cl)2 (thf)2 ]2 (2; H2 L2 =N,N'-bis(3,5-di-tert-butylsalicylidene)ethylenediamine) are reported. These two complexes have two short Dy-O(PhO) bonds that exhibit angles of ∼90° for 1 and ∼143° for 2, leading to clear slow relaxation of the magnetization for 2 and not for 1. Compound 2 has a near-identical core to the recently reported compound [Dy2 (L3 )2 (µ-Cl)2 (thf)2 ] (3; H2 L3 =N-(2-pyridylmethyl)-N,N-bis(2'-hydroxy-3',5'-di-tert-butylbenzyl)amine). The only substantial difference is the relative angle of the two O(PhO) -Dy-O(PhO) vectors, which is collinear in 2 owing to inversion symmetry and ∼68° in 3 due to a molecular C2 axis. It is shown that this subtle structural difference leads to large differences in the dipolar ground states, giving rise to open magnetic hysteresis for 3 and not for 2.

How important is the linearity assumption in a sample size calculation for a randomised controlled trial where treatment is anticipated to affect a rate of change?

BACKGROUND: For certain conditions, treatments aim to lessen deterioration over time. A trial outcome could be change in a continuous measure, analysed using a random slopes model with a different slope in each treatment group. A sample size for a trial with a particular schedule of visits (e.g. annually for three years) can be obtained using a two-stage process. First, relevant (co-) variances are estimated from a pre-existing dataset e.g. an observational study conducted in a similar setting. Second, standard formulae are used to calculate sample size. However, the random slopes model assumes linear trajectories with any difference in group means increasing proportionally to follow-up time. The impact of these assumptions failing is unclear. METHODS: We used simulation to assess the impact of a non-linear trajectory and/or non-proportional treatment effect on the proposed trial's power. We used four trajectories, both linear and non-linear, and simulated observational studies to calculate sample sizes. Trials of this size were then simulated, with treatment effects proportional or non-proportional to time. RESULTS: For a proportional treatment effect and a trial visit schedule matching the observational study, powers are close to nominal even for non-linear trajectories. However, if the schedule does not match the observational study, powers can be above or below nominal levels, with the extent of this depending on parameters such as the residual error variance. For a non-proportional treatment effect, using a random slopes model can lead to powers far from nominal levels. CONCLUSIONS: If trajectories are suspected to be non-linear, observational data used to inform power calculations should have the same visit schedule as the proposed trial where possible. Additionally, if the treatment effect is expected to be non-proportional, the random slopes model should not be used. A model allowing trajectories to vary freely over time could be used instead, either as a second line analysis method (bearing in mind that power will be lost) or when powering the trial.