Linear Adjustment Research Articles

Proteomic signatures of physical, cognitive, and imaging outcomes in multiple sclerosis.

A quantitative measurement of serum proteome biomarkers that would associate with disease progression endpoints can provide risk stratification for persons with multiple sclerosis (PwMS) and supplement the clinical decision-making process. In total, 202 PwMS were enrolled in a longitudinal study with measurements at two time points with an average follow-up time of 5.4 years. Clinical measures included the Expanded Disability Status Scale, Timed 25-foot Walk, 9-Hole Peg, and Symbol Digit Modalities Tests. Subjects underwent magnetic resonance imaging to determine the volumetric measures of the whole brain, gray matter, deep gray matter, and lateral ventricles. Serum samples were analyzed using a custom immunoassay panel on the Olink™ platform, and concentrations of 18 protein biomarkers were measured. Linear mixed-effects models and adjustment for multiple comparisons were performed. Subjects had a significant 55.6% increase in chemokine ligand 20 (9.7 pg/mL vs. 15.1 pg/mL, p < 0.001) and neurofilament light polypeptide (10.5 pg/mL vs. 11.5 pg/mL, p = 0.003) at the follow-up time point. Additional changes in CUB domain-containing protein 1, Contactin 2, Glial fibrillary acidic protein, Myelin oligodendrocyte glycoprotein, and Osteopontin were noted but did not survive multiple comparison correction. Worse clinical performance in the 9-HPT was associated with neurofilament light polypeptide (p = 0.001). Increases in several biomarker candidates were correlated with greater neurodegenerative changes as measured by different brain volumes. Multiple proteins, selected from a disease activity test that represent diverse biological pathways, are associated with physical, cognitive, and radiographic outcomes. Future studies should determine the utility of multiple protein assays in routine clinical care.

The existence, uniqueness and stability of steady state for a class of first-order difference equations with application to the housing market dynamic

We study the existence, uniqueness and stability of the steady state for the dynamic described by a class of first-order difference equations. We then apply the result to analyse a housing market where the supply is linear and demand is a bounded and monotone decreasing function of price, derived from households’ optimization behaivour. Under two linear price adjustment mechanisms, we prove the existence and uniqueness of an equilibrium, which is independent of the mechanisms. That is, the house price converges to a same steady state where it clears the market under both mechanisms. The result is general in the sense that we do not need to specify a particular form of demand function. Besides, the same approach can be utilized to analyse the dynamics of other markets.

Review of World Rugby’s Test Method 01 head injury criteria: Procedure analysis and optimisation

Rugby is a close-contact sport in which players occasionally fall headfirst to the ground during scrums and tackles. Because head impacts represent an obvious threat to players’ integrity and safety, World Rugby, Rugby’s International Governing Body, developed a test method named Test Method 01 to evaluate the capacity of the playing surface to mitigate head impacts by determining the critical fall height (CFH). The aim of this study is to analyse World Rugby’s current Test Method 01 head injury criteria (HIC), which consider a field as unsafe if the CFH is below 1.3 m. To make this analysis, a pilot study was performed on seven artificial turf rugby fields. At each field, a three-drop procedure was performed to estimate the initial CFH (CFH0). Subsequently, the procedure was repeated on each surface at 50-mm intervals, from 0.6 m below to 0.6 m above CFH0. All possible combinations of four height–HIC data pairs with two height values below and above 1000 HIC were obtained. A comparison was performed between the linear adjustment, currently prescribed in Test Method 01 to calculate the CFH0, and the quadratic adjustment. In particular, the percentage of outliers obtained when applying both the linear and quadratic adjustment and the robustness of the regressions were investigated. The results show that the current Test Method 01 can be improved by applying two main modifications: first, replacing the linear adjustment with a quadratic adjustment, and second, adapting the current test restrictions by maintaining the maximum difference between the highest and the lowest drop heights in 1.00 m, increasing the minimum difference between consecutive drop heights from 0.15 to 0.20 m and removing the current prohibition on obtaining HIC values close to 1000.

Modern Control of a Power Supply Based on a Matrix Converter for Water Disinfection by UVC Radiation

Water, an essential resource, has been facing gradual deterioration in quality over an extended period. Water treatment has emerged as a critical concern, with a long-standing acknowledgment of the importance of preserving and appreciating this precious resource. UV-C technology has proven to be an ideal solution that effectively addresses these twin needs. The core principle of UV bactericidal treatment revolves around generating ultraviolet rays within a treatment chamber filled with water. Consequently, ensuring a dependable power source for low-pressure mercury-argon discharge lamps has become imperative to guarantee the efficiency of UV-C disinfection.The primary goal of this study is to supply our discharge lamp with a current source that produces a sinusoidal current at its output, featuring a frequency of 50 kHz and an effective value of 0.65 A. Electronic ballasts enable lamps to enhance radiation quality by operating at high frequencies, and the selection of a power supply is a response to this specific challenge.The aim of this research centers on the utilization of a single-phase matrix converter. The bidirectional switching cells within this converter offer frequency-related advantages. To achieve the desired magnitude and frequency, we employed a PWM control strategy. Subsequently, we implemented a linear current adjustment approach using two controllers: a Proportional-Integral (PI) controller and a Generalized Predictive Control (GPC) in the RST polynomial form. This was done to ensure a high-quality current source with the desired waveform and low Total Harmonic Distortion (THD).The research outcomes have led to environmental simulations conducted using Matlab/Simpower system and Matlab/Simulink.

A High-Precision Bandgap Reference with Chopper Stabilization and V-Curve Compensation Technique.

The MEMS sensor converts the physical signal of nature into an electrical signal. The output signal of the MEMS sensor is so weak and basically in the low-frequency band that the MEMS sensor interface circuit has a rigorous requirement for the noise/offset and temperature coefficient, especially in the bandgap reference block. However, the traditional amplifier has low-frequency noise and offset voltage, which will decrease the precision of the bandgap reference. In order to satisfy the need of the MEMS sensor interface circuit, a high-precision and low-noise bandgap reference is proposed in this paper. A novel operational amplifier with a chopper-stabilization technique is adopted to reduce offset and low-frequency noise. At the same time, the V-curve compensation circuit is used to realize the second-order curvature compensation. The circuit is implemented under the 0.18 μm standard of the CMOS process. The test result shows that the temperature coefficient of the bandgap is 2.31 ppm/°C in the range of -40-140 °C, while the output voltage noise is only 616 nV/sqrt(Hz)@1 Hz and the power-supply rejection ratio is 73 dB@10 kHz. The linear adjustment rate is 0.33 mV/V for supply voltages of 1.2-1.8 V at room temperature, the power consumption is only 107 μW at 1.8 V power supply voltage, and the chip active area is 0.21 × 0.28 mm2.

Secondary metabolites of Urochloa ruziziensis on growth, nodulation, and spectral responses of soybean

Ruzigrass (Urochloa ruziziensis) is a widely cultivated plant alongside soybeans, particularly in integrated crop and livestock systems, due to its fast growth and adaptability to different conditions. This study aimed to assess the impact of secondary metabolites found in ethanolic extract from ruzigrass on soybean growth, nodulation, spectral responses, and soil microbiological attributes. The ethanolic extract of ruzigrass presents total concentration of flavonoids (852.5 µg g−1), including naringenin and kaempferol. Increasing doses (100, 200, 300, and 400 kg ha−1) of the extract were then applied to the soil in a greenhouse to cultivate soybean plants. The spectral analysis indicated that higher doses of ruzigrass extract enhanced photochemical reflectance, chlorophyll absorption, and total chlorophyll indices. However, the normalized differential vegetative index decreased in response to the treatments. Generally, increasing doses of ruzigrass extract led to linear improvements in plant height, leaf area, shoot dry mass, pod count, nodule count, nitrogen content, and soil microbial activity. On the other hand, root dry massand relative chlorophyll content decreased with higher doses of the extract. In conclusion, the application of Urochloa ruziziensis extract, containing secondary metabolites caused a reduction in root development and an increase in spectral indices related to abiotic stresses in soybeans. There was an increase in the biological attributes of the soil with a significant, increasing linear adjustment in the doses of ruzigrass extract applied, as well as in the soybean production components.

Design of acceleration control schedule for adaptive cycle engine based on direct simulation model

To design the optimum acceleration control schedule for the Adaptive Cycle Engine (ACE) in the full flight envelope, this paper establishes a direct simulation model of the ACE transient state. In this model, geometric parameters are used to replace the component state parameters. The corresponding relationship between geometric parameters and component state parameters is determined by sensitivity analysis. The geometric variables are controlled when the geometric adjustment speed exceeds the limit, and at the same time the corresponding component state parameters are iterated. The gradient optimization algorism is used to optimize the ground acceleration process of ACE, and the control schedule in terms of operating point of compression components and corrected acceleration rate is used as the full-envelope acceleration control schedule based on the similarity principle. The acceleration control schedules of the triple-bypass mode and the double-bypass mode are designed in this paper. The acceleration processes under various flight conditions are simulated using the acceleration control schedules. Compared with the acceleration process with the linear geometric adjustment schedule, the acceleration performance of ACE is improved by the acceleration control schedule, with the impulse of the acceleration process of the triple-bypass mode being increased by 8.7%–12.3% and the impulse of the double-bypass mode acceleration process being increased by 11.8%–14.1%.

Optimization method of 3D reconstruction of metal cultural relics based on 3D laser scanning data reduction

AbstractThe extraction effect and feature matching are poor in the three‐dimensional reconstruction of metal cultural relics, which leads to a poor reconstruction effect. Therefore, an optimization method of three‐dimensional reconstruction of metal cultural relics based on 3D laser scanning data reduction is proposed. The overall technical design route of the method is shown as follows. Based on this model, the 3D laser scanning method is used to collect 3D images of metal artefacts, combined with colour space and 2D entropy detection methods to pre‐process 3D images, and feature matching of point clouds is carried out to extract and optimize the significant value of superpixels, and a 3D reconstructed visual model is constructed. Affine transformation is used to obtain the affine invariant moment of the structural light parameters of the visual feature lines of metal cultural relics. The light stability adjustment of the three‐dimensional reconstruction of metal cultural relics is realized by using the linear structural light adjustment method in the HSV colour space. The rigid and non‐rigid registration methods are introduced to match the point cloud. The product quantization algorithm is used to linearize the error function, and the block feature detection and matching model of spatial image is obtained. The noise number is judged by the threshold value, and the three‐dimensional reconstruction technology is combined to realize the three‐dimensional reconstruction of metal relics. The simulation results show that this method has good visual expression ability, high feature recognition rate, and improves the three‐dimensional reconstruction ability of metal relics.

Business cycles, sectoral price stabilization, and climate change mitigation: A model of multi-sector growth in the tradition of the Bielefeld disequilibrium approach

Sectoral price stabilization is critical in the pressing context of de-globalization and the climate crisis. Strategic price controls may be effective in reducing economic volatility, but fail to curb emissions, unlike quantity controls such as rationing consumption. In contrast, carbon pricing may accelerate decarbonization, but generate inflationary pressures. In order to evaluate the effectiveness of sector-oriented policies in stabilizing sectoral prices and accelerating the low-carbon transition at the same time, this paper employs a novel environmentally-extended, data-driven dynamic model of multi-sector growth based on the Bielefeld disequilibrium approach to the microeconomic stability of competitive economies. The general composite model allows to empirically characterize the network structure and intensity of dynamic price-quantity interactions at the sector level, which capture heterogeneous firm behavior by integrating long-run Walrasian price and classical quantity dynamics coupled with short-run Keynesian features in the form of target rate of return pricing and demand-led investment. A Bayesian hierarchical model on US BEA data empirically estimates the linear adjustment coefficients and stable combinations are computed. The US economy is shown to feature a highly hierarchical network structure of intermediate production that is particularly vulnerable to micro-economic shocks driven by wars and climate change. Tax-subsidy schemes are shown to be the most effective in stabilizing sectoral prices and economy-environment interactions.

Experimental Investigation of the Dynamic Response of a Flat Blade with Dual Dry Friction Dampers

One test rig comprising two blades and dual under-platform dampers (UPDs) was built to enhance the understanding of the dynamic response behavior of blades with dual UPDs. A turnbuckle was applied to enable the smooth and uninterrupted linear adjustment of the normal load on the dual UPDs. Non-contact vibration-response measurements were achieved through eddy-current displacement sensors. Contact excitation was employed using an electromagnetic exciter to determine the magnitude of the excitation load, which was measured using a force sensor mounted on the excitation rod. A feedback system was established to maintain a constant magnitude of the excitation force throughout the excitation process. The chosen experimental variables include the normal load, the amplitude of the excitation force, the effective contact area, and the position of the damper action. The frequency response function of the blade under various experimental parameters was obtained through frequency sweeping under sinusoidal excitation. The influence of each parameter on the dynamic characteristics of blades was studied. The results demonstrate that the double-layer damping system offers distinct advantages over its single-layer counterpart. The upper damping has a wider frequency-adjustment range and a lower resonance amplitude and takes a larger share of the damping efficiency.

An LDO without a Capacitor Required in Applications

Linear voltage regulator with low voltage dropout is widely used in DC/DC circuits because of the advantages of simple structure, low noise, high efficiency, and small package size. In this paper, high stability LDO linear voltage regulator with low static current is designed. By using a voltage detection module, the pass transistor in the regulator can be quickly regulated or switched on and off under load transient conditions. In addition, the stability of the LDO is improved by using an NMOS pass transistor and diode clamp architecture. The test results show that the typical values of linear adjustment and load adjustment of the voltage regulator are 20 mV and 200 mV, respectively. The maximum output current is 60 mA, the load current is 20 mA, and the output pressure difference under 4.8 V output voltage is 210 mV. Compared with traditional LDO, although the output current is not the maximum, the difference and stability of output pressure are greatly improved.

Pendulum tuned mass damper (PTMD) with geometric nonlinear dampers for seismic response control

In engineering applications, the geometric nonlinear (GN) arrangement of pendulum-tuned mass dampers (PTMDs) may induce the damping force to deviate from its intended state. Therefore, this study extends the scope of the structural control strategy by introducing a pendulum-tuned mass damper considering geometric nonlinear dampers (GND). Specifically, the damper developed in this study, termed PTMD with GND, is an inconspicuous pendulum-type tuned mass damper with different GN settings in the initial state. A nonlinear mathematical model of the PTMD with GND is developed, identifying its significant nonlinear characteristics, particularly the "unavailable" locations. The stochastic linearization method (SLM) is adopted to simplify the nonlinear model using the Kanai-Tajimi modified spectrum. The SLM agrees well with the numerical results obtained using the Monte Carlo simulation method. Furthermore, the control strategy of PTMD with GND is proposed with the consideration of filtered random excitation. Several numerical cases have been conducted to investigate the availability of PTMD with GND and the proposed optimal design strategy under 178 real seismic excitations. The results show that the PTMD with GND is nearly as effective as the ideal transitional TMD in mitigating the seismic response of the primary structure and more effective than the inverted rough linear adjustment. It can be concluded that the proposed optimal design strategy for the PTMDs with GND efficiently suppressed the structural vibration through multiple performance indices and used the nonlinearity of the damping mechanism of the GND to provide a sufficient damping energy dissipation effect adaptively.

The Association between Serum Adiponectin Levels and Endothelial Function in Non-Dialysis-Dependent Chronic Kidney Disease Patients.

Adiponectin is the richest human circulating adipokine with anti-inflammatory, antioxidant, and insulin-sensitizing effects. We evaluated the association between serum adiponectin levels and endothelial function in chronic kidney disease (CKD) patients, obtaining fasting blood samples from 130 non-dialysis CKD subjects. We measured the endothelial function-represented by the vascular reactivity index (VRI)-via non-invasive digital thermal monitoring, and serum adiponectin concentrations by enzyme immunoassay kits. A total of 22 (16.9%), 39 (30.0%), and 69 (53.1%) patients had poor (VRI < 1.0), intermediate (1.0 ≤ VRI < 2.0), and good (VRI ≥ 2.0) vascular reactivity. Elevated serum blood urea nitrogen (BUN) level was negatively correlated with VRI values, but serum adiponectin and estimated glomerular filtration rate were positively associated with VRI values by univariate linear regression analysis. After applying multivariate stepwise linear regression analysis adjustment, the significantly positive association of adiponectin (p < 0.001), and the significantly negative association of log-BUN (p = 0.021) with VRI values in CKD subjects remained. In an animal study using in vitro blood-vessel myography, treatment with adiponectin enhancing acetylcholine-mediated vasorelaxation in 5/6 nephrectomy CKD mice. Our study results indicated that adiponectin concentration was positively associated with VRI values and modulated endothelial function in non-dialysis CKD patients.

A linear adjustment-based approach to posterior drift in transfer learning.

We present new models and methods for the posterior drift problem where the regression function in the target domain is modelled as a linear adjustment, on an appropriate scale, of that in the source domain, and study the theoretical properties of our proposed estimators in the binary classification problem. The core idea of our model inherits the simplicity and the usefulness of generalized linear models and accelerated failure time models from the classical statistics literature. Our approach is shown to be flexible and applicable in a variety of statistical settings, and can be adopted for transfer learning problems in various domains including epidemiology, genetics and biomedicine. As concrete applications, we illustrate the power of our approach (i) through mortality prediction for British Asians by borrowing strength from similar data from the larger pool of British Caucasians, using the UK Biobank data, and (ii) in overcoming a spurious correlation present in the source domain of the Waterbirds dataset.

Fibonacci Level Adjustment for Optimizing Player’s Performance and Engagement

Players’ engagement intensity in computer games is influenced by the level of difficulty the game offers. Traditional game-level plots adopt linear increases that sometimes do not match the users’ skill growth, causing boredom and hampering the users’ further skill growth. In this study, a nonlinear level adjustment scenario was proposed based on the Fibonacci sequence that provides gradual increases in the early stages of the games but more drastic changes in later phases. Here, the game’s difficulty level was automatically decided by a machine learning method. To test the proposed method, comparisons between four level adjustments in computer games: traditional plots, self-selected plots, linear adaptive plots, and the proposed nonlinear adaptive plots were run. The experiment was carried out with 40 testers. The experiment results show that the best player’s peak level in the proposed nonlinear adjustment was twice as high as that of linear adjustment. Also, the number of stages required to reach the peak under the proposed scenario was half that of linear games. This high playing performance goes hand in hand with deep playing engagement. The results demonstrate the efficiency of the proposed level adjustment algorithm.

Extraction of spin-averaged rovibrational transition frequencies in HD+ for the determination of fundamental constants

We present a comprehensive analysis of all currently available high-accuracy frequency measurements of rotational and rovibrational transitions in the hydrogen molecular ion . Our analysis utilises the theoretically calculated hyperfine structure to extract the values of three spin-averaged transition frequencies through a global linear least-squares adjustment that takes into account theory-induced correlations between the different transitions. We subsequently use the three spin-averaged transition frequencies as input data in a second adjustment which employs precise theoretical expressions for the transition frequencies, written as a function of the proton, deuteron and electron relative atomic masses, the Rydberg constant, and the proton and deuteron charge radii. Our analysis shows that the data may significantly improve the value of the electron relative atomic mass and the proton-electron mass ratio, in particular if combined with recent high-precision measurements of particle atomic masses and mass ratios obtained from Penning traps.

Bibliometric analysis of holographic data storage literature

Objectives. Snapshots of data can be stored in a holographic medium at varying depths. Data can be written via a spiral data channel in spinning holographic media in the form of circular disks like CDs or DVDs. This data is then read by shining a reference beam through the refraction following writing. However, holographic storage is distinct from CD/DVD media in the sense that information is encoded in all three dimensions. Two-dimensional data is written using a single laser beam that spirals around the material. Prototype holographic storage solutions use minuscule cones formed by individual snapshots or pages to store one million pixels. As compared with magnetic disks and tapes, which have a finite lifespan of 50 years at most, the longevity and dependability of optical media storage is advantageous for long-term archiving. Holographic technology allows for the portability of data-intensive media such as broadcast or high-definition video. However, the shelf life of holographic media remains low due to its sensitivity to light. The primary goals of most storage devices are more storage space and faster data transport. Holographic storage devices have the potential to outperform traditional optical storage devices both in terms of capacity and performance. The present paper aims to evaluate the current international research trends in Holographic Data Storage (HDS) and produce a graphical mapping of co-authorship and countries.Methods. The major outputs of the dataset were authors, document type, publication, institution, nation, and citations. After exporting 1052 data sources, HistCite software was used to analyze the citations; visualization mapping was carried out using VOSviewer software and R programming language for the analysis of the authorcountry-title association on Holographic Storage Devices.Results. The most prominent authors, papers, journals, organizations, and nations in the field of HDS were identified in HistCite. Then, four clusters were investigated using VOSviewer based on author keywords, citation collaboration networks among different organizations, countries, and the HDS co-authorship network.Conclusions. During the study period from 2000–2020 (21 years), 4636 authors contributed to 1052 publications. The highest number of publications was in 2009, with a linear adjustment of R2 = 0.0136. The most prolific author, Lee J., published 3.14% of the articles on this subject. In terms of country distribution, Japan took first-place ranking, claiming 16.54% of the total number of articles. The “holographic” keyword was used in 62.55% of the articles.

Operationalizing the centiloid scale for [18F]florbetapir PET studies on PET/MRI.

The Centiloid scale aims to harmonize amyloid beta (Aβ) positron emission tomography (PET) measures across different analysis methods. As Centiloids were created using PET/computerized tomography (CT) data and are influenced by scanner differences, we investigated the Centiloid transformation with data from Insight 46 acquired with PET/magnetic resonanceimaging (MRI). We transformed standardized uptake value ratios (SUVRs) from 432 florbetapir PET/MRI scans processed using whole cerebellum (WC) and white matter (WM) references, with and without partial volume correction. Gaussian-mixture-modelling-derived cutpoints for Aβ PET positivity were converted. The Centiloid cutpoint was 14.2 for WC SUVRs. The relationship between WM and WC uptake differed between the calibration and testing datasets, producing implausibly low WM-based Centiloids. Linear adjustment produced a WM-based cutpoint of 18.1. Transformation of PET/MRI florbetapir data to Centiloids is valid. However, further understanding of the effects of acquisition or biological factors on the transformation using a WM reference is needed. Centiloid conversion of amyloid beta positron emission tomography (PET) data aims to standardize results.Centiloid values can be influenced by differences in acquisition.We converted florbetapir PET/magnetic resonance imaging data from a large birth cohort.Whole cerebellum referenced values could be reliably transformed to Centiloids.White matter referenced values may be less generalizable between datasets.

Realizing multicolor tunable photoluminescence in La2MgTiO6: Tb3+, Eu3+ phosphors via energy transfer and application for white light-emitting diodes

The achievement of multiple emission color phosphors has a significant importance in screen display, lighting devices, and multicolor imaging, but it still faces formidable challenges. In this work, double perovskite La2MgTiO6: Tb3+, Eu3+ phosphors with tunable emissions are designed and successfully synthesized. The obtained phosphors can emit intense green (Tb3+), red (Eu3+), and yellow emissions (Tb3+/Eu3+) via varying the co-doping concentration of Tb3+ and Eu3+. The CIE coordinates exhibit an excellent linear behavior in La2MgTiO6: Tb3+, Eu3+, revealing the possibility of linear adjustment of multiple emission colors. Detailed material characterization demonstrates that the multicolor tunable emission originates from energy transfer between Tb3+ and Eu3+. The decay dynamics analysis suggests that the multipole interaction between Tb3+ and Eu3+ is quadrupole-quadrupole interaction. A white light-emitting diode device with color rendering index of 84.7, correlated color temperature of 4684 K, and CIE coordinate of (0.3472, 0.3083) is fabricated by combining La2MgTiO6: Tb3+, Eu3+ yellow phosphor and BaMgAl10O17: Eu2+ blue phosphor. Our results reveal that La2MgTiO6: Tb3+, Eu3+ phosphors are promising luminescent materials in white light-emitting diodes.

A novel T-shaped high-power waveguide phase shifter with continuous linear phase adjustment.

A novel T-shaped high-power waveguide phase shifter is investigated in this paper. The phase shifter consists of straight waveguides, four 90° H-bend waveguides, a stretching metal plate, and a metal spacer linked with the stretching metal plate. The entire structure for the phase shifter is symmetrical along both sides of the metal spacer. The phase-shifting principle for the phase shifter is to change the microwave transmission path by moving the stretching metal plate and then realize the linear phase adjustment. An optimal design approach of the phase shifter based on the boundary element method is described in detail. On this basis, a T-shaped waveguide phase shifter prototype with a center frequency of 9.3GHz is designed. Simulation results show that the phase shifters can achieve 0°-360° linear phase adjustment by altering the distance of the stretched metal plate to 24mm, and the efficiency of power transmission is more than 99.6%. In the meanwhile, experiments were conducted and the test results are in good agreement with simulation results. The return loss is more than 29 dB, and the insertion loss is less than 0.3 dB at 9.3GHz in the entire phase-shifting range.