Mean Phase Error Research Articles

Active on-site calibration technology of current transformer based on non-rated frequency current injection.

This paper proposes an active on-site calibration method through background current cancellation and non-rated current injection. It can measure the error of the current transformer in service from 1% to 120% rated current percentage without power supply interruption. In order to establish the error relationship between rated frequency and arbitrary frequency, a theoretical analysis of current transformer calibration at the arbitrary frequency has been developed by means of the equivalent circuit. It describes a method to determine the phase angle and ratio errors of the measuring transformers at arbitrary frequencies on the basis of the calibrated error values at rated frequency. To prove the theoretical analysis, an experimental validation was carried out. The experimental results demonstrate that this active onsite calibration is a valid tool for the evaluation of current transformer performances. The calibration results showed that, for both cases (non-rated frequency calibration and mixing frequency calibration), the difference between mean ratio error and rated frequency ratio error was lower than 0.01%, and the difference between mean phase error and rated frequency phase error was lower than 1', which meets the requirement of the 0.2 accuracy class calibration.

Acute Eye-Tracking Changes Correlated With Vestibular Symptom Provocation Following Mild Traumatic Brain Injury.

To quantify norms and changes in eye-tracking proficiency, and determine vestibular symptom correlations in varsity college athletes following acute mild traumatic brain injury (mTBI). We hypothesized that mTBI impacts central coordination between the vestibular and oculomotor systems with resultant changes in eye-tracking proficiency that are correlated with vestibular symptom provocation. Retrospective cohort study. Sports medicine care at a single institution. One hundred and nineteen college athletes diagnosed with mTBI by a physician between 2013 and 2019. N/A. Standard deviation of tangential error, standard deviation of radian error, mean phase error, and horizontal gain from virtual reality-based, circular eye-tracking goggles used at baseline and within 72 hours post-mTBI. Headache, dizziness, nausea, and fogginess provocation after the Vestibular Ocular Motor Screening (VOMS) smooth pursuits subtest compared with pretest baseline, assessed within 72 hours post-mTBI. One hundred and nineteen college athletes (N = 56 women and 63 men) aged 18 to 24 years sustained a total of 177 mTBI. Forty-four percent of athletes displayed abnormal eye-tracking on at least 1 eye-tracking measure following acute mTBI compared with their baseline. From the VOMS, horizontal gain showed medium-sized to large-sized positive correlations with headache ( r = 0.34) and dizziness ( r = 0.54), respectively. Mean phase error showed a medium-sized negative correlation with nausea ( r = -0.32) on the VOMS. Eye-tracking proficiency was impaired and correlated with vestibular symptom provocation following acute mTBI in college athletes. Future research should examine eye-tracking proficiency testing in other acute care settings to support mTBI diagnosis.

Refining Protein Envelopes with a Transition Region for Enhanced Direct Phasing in Protein Crystallography

In protein crystallography, the determination of an accurate protein envelope is of paramount importance for ab initio phasing of diffraction data. In our previous work, we introduced an approach to ascertain the protein envelope by seeking an optimal cutoff value on a weighted-average density map. In this paper, we present a significant advancement in our approach by focusing on identifying a transition region that demarcates the boundary between the protein and solvent regions, rather than relying solely on a single cutoff value. Within this transition region, we conducted a meticulous search for the protein envelope using a finer map and our proposed transition hybrid input–output (THIO) algorithm. Through this improvement, we achieved a refined protein envelope even when starting from random phases, enabling us to determine protein structures with irregular envelopes and successfully phase crystals with reduced solvent contents. To validate the efficacy of our method, we conducted tests using real diffraction data from five protein crystals, each containing solvent contents ranging from 60% to 65%. Solving these structures through conventional direct methods proved difficult due to the limited solvent content. The mean phase error obtained through our proposed method was about 30°. The reconstructed model matched with the structure in the protein data bank with a root mean square deviation (r.m.s.d.) of about 1 Å. These results serve as compelling evidence that the utilization of the proposed transition region in conjunction with the THIO algorithm contributes significantly to the construction of a reliable protein envelope. This, in turn, becomes indispensable for the direct phasing of protein crystals with lower solvent contents.

An Active Reconfigurable Intelligent Surface Utilizing Phase-Reconfigurable Reflection Amplifiers

Active reconfigurable intelligent surfaces (RISs) have recently been proposed to complement and generalize passive RIS. In this work, the design for an active RIS based on phase-reconfigurable reflection amplifiers is proposed. The proposed active RIS elements’ design consists of a two-layer patch antenna and a phase-reconfigurable reflection amplifier that is realized by a cascade of a phase shifter and a reflection amplifier. Theoretical and numerical analyses are used to quantify key parameters that need to be met in the design of the reflection amplifier and phase shifters. These show that a tradeoff between the reflection amplifier’s gain and the phase shifter’s return and insertion loss is required to be balanced to obtain a stable and effective overall design. In particular, a reflection amplifier with about 13-dB gain and a 2-bit phase shifter with only about 1.9-dB insertion loss and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$-$</tex-math> </inline-formula> 25-dB return loss are designed. The final RIS element obtains 8.5-dB gain with four reconfigurable phases ranging from 0 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{\circ}$</tex-math> </inline-formula> to 360 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{\circ}$</tex-math> </inline-formula> with small root mean square (rms) gain and phase errors. An active RIS can be constructed by concatenating these elements together, and an efficient analytical method to calculate the scattered pattern by the active RIS is also proposed. Experimental results for a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2$</tex-math> </inline-formula> <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times$</tex-math> </inline-formula> <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2$</tex-math> </inline-formula> element active RIS prototype are also provided. These show that the active RIS provides received powers around 8.5 dB higher than that from using an equivalent passive RIS. The results demonstrate the feasibility of achieving gain in active RISs and help demonstrate their promise as a technology for future high-capacity wireless communication systems.

Direct Phasing of Coiled-Coil Protein Crystals

Coiled-coil proteins consisting of multiple copies of helices take part in transmembrane transportation and oligomerization, and are used for drug delivery. Cross-alpha amyloid-like coiled-coil structures, in which tens of short helices align perpendicular to the fibril axis, often resist molecular replacement due to the uncertainty to position each helix. Eight coiled-coil structures already solved and posted in the protein data bank are reconstructed ab initio to demonstrate the direct phasing results. Non-crystallographic symmetry and intermediate-resolution diffraction data are considered for direct phasing. The retrieved phases have a mean phase error around 30∼40°. The calculated density map is ready for model building, and the reconstructed model agrees with the deposited structure. The results indicate that direct phasing is an efficient approach to construct the protein envelope from scratch, build each helix without model bias which is also used to confirm the prediction of AlphaFold and RosettaFold, and solve the whole structure of coiled-coil proteins.

E‐band broadband digital controlled phase‐inverting variable gain amplifier in 65‐nm CMOS

This letter reports an E-band phase-inverting variable gain amplifier in 65-nm complementary metal-oxide-semiconductor (CMOS) technology. A fractional bit based structure with replica cells is proposed to minimise the phase error and ensure the tuning accuracy between different gain modes. This structure has 9-bits digital-controlled amplifiers and allows 180° phase shifting. The implemented phase-inverting variable gain amplifier achieves 16 dB tuning range and 0.5 dB tuning step at 80 GHz. The root mean square (RMS) gain and phase errors across −3 dB bandwidth (i.e. 72–87 GHz) are less than 0.3 dB and 2.7°, respectively. The phase-inverting variable gain amplifier consumes 8 mW at 1 V supply voltage.

Effect Of Practice And Game-Related Impacts On Common Indicators Of Concussion: A Pilot Study

Previous studies have suggested that football players not clinically diagnosed with concussion may still demonstrate differences in balance and neurocognitive performance by end of season. Clinically this is important as it indicates the athlete with sub-clinical injuries that may contribute to long-term deficits. PURPOSE: A pilot study to determine if non-concussive impacts sustained during normal play at NCAA Division I football practices and spring season scrimmage are sufficient to elicit detectable changes in oculomotor (OM) and balance performance. METHODS: 23 NCAA Division I football players were recruited to this pilot study during the 2019 spring football season. Questionnaires were used to collect demographic information. Portable virtual reality equipment was utilized to measure OM performance of smooth pursuit, saccade, and vestibular ocular reflex (VOR). BESS was utilized to measure balance performance. Assessments were administered at baseline, 24-48 hours after 3 practices, and the spring season scrimmage. Shapiro-Wilkes analysis was used to assess changes in balance and OM skills in subjects across the pilot project. RESULTS: Of the 23 recruited subjects, 7 (30%) completed all assessments; however, there were missing data observations for the 7 subjects who completed all 5 assessment points. There was no significant change in balance performance (p = 0.375); one variable of smooth pursuit testing (mean phase error of left eye) demonstrated near significant changes (p = 0.0625). There was no significant change in any variables for horizontal or vertical VOR, while, one variable of horizontal and vertical saccade testing (accuracy x of left eye) demonstrated near significant changes (p = 0.0625). CONCLUSION: We found no significant detectable changes in balance and OM performance in this pilot study.

Complex SAR Image Compression Using Entropy‐Constrained Dictionary Learning and Universal Trellis Coded Quantization

In this paper, an Entropy-constrained dictionary learning algorithm (ECDLA) is introduced for efficient compression of Synthetic aperture radar (SAR) complex images. ECDLA RI encodes the Real and imaginary parts of the images using ECDLA and sparse representation, and ECDLA AP encodes the Amplitude and phase parts respectively. When compared with the compression method based on the traditional Dictionary learning algorithm (DLA), ECDLA RI improves the Signal-to-noise ratio (SNR) up to 0.66dB and reduces the Mean phase error (MPE) up to 0.0735 than DLA RI. With the same MPE, ECDLA AP outperforms DLA AP by up to 0.87dB in SNR. Furthermore, the proposed method is also suitable for real-time applications.

A 220–320-GHz Vector-Sum Phase Shifter Using Single Gilbert-Cell Structure With Lossy Output Matching

This paper presents a wideband vector-sum phase shifter (VSPS) that operates over the entire WR-3 band (220-320 GHz). Compared to conventional VSPSs with double Gilbert cells, the proposed phase shifter employs a single Gilbert-cell structure for vector modulation. This reduces the output current combining ratio from 8:2 to 4:2, and boosts the impedance at the combining node, thus facilitating wideband output matching at upper millimeter-wave and terahertz bands. The simplified structure leads to a reduction in dc power consumption and chip area without sacrificing the 360 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">°</sup> phase-shifting property. Lossy matching is applied at the Gilbert-cell output to further increase bandwidth and stability at the expense of relatively high loss. The phase shifter is implemented using a 250-nm InP DHBT technology that provides f T and f max exceeding 370 and 650 GHz, respectively. The measurements exhibit a wideband phase shift with continuous 360 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">°</sup> coverage and average insertion loss ranging from 11.8 to 15.6 dB for the entire WR-3 band. The root mean square amplitude and phase error among different phase states are less than 1.2 dB and 10.2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">°</sup> , respectively. The input-referred 1-dB compression is measured at 0.7 dBm on average. The dc power consumption is 21.8-42.0 mW at different phase states.

Direct phase selection of initial phases from single-wavelength anomalous dispersion (SAD) for the improvement of electron density and ab initio structure determination.

Optimization of the initial phasing has been a decisive factor in the success of the subsequent electron-density modification, model building and structure determination of biological macromolecules using the single-wavelength anomalous dispersion (SAD) method. Two possible phase solutions (φ1 and φ2) generated from two symmetric phase triangles in the Harker construction for the SAD method cause the well known phase ambiguity. A novel direct phase-selection method utilizing the θ(DS) list as a criterion to select optimized phases φ(am) from φ1 or φ2 of a subset of reflections with a high percentage of correct phases to replace the corresponding initial SAD phases φ(SAD) has been developed. Based on this work, reflections with an angle θ(DS) in the range 35-145° are selected for an optimized improvement, where θ(DS) is the angle between the initial phase φ(SAD) and a preliminary density-modification (DM) phase φ(DM)(NHL). The results show that utilizing the additional direct phase-selection step prior to simple solvent flattening without phase combination using existing DM programs, such as RESOLVE or DM from CCP4, significantly improves the final phases in terms of increased correlation coefficients of electron-density maps and diminished mean phase errors. With the improved phases and density maps from the direct phase-selection method, the completeness of residues of protein molecules built with main chains and side chains is enhanced for efficient structure determination.

SU-D-105-05: Independent Evaluation of Respiratory-Gated Treatments Using In-House Quality Assurance Tool

Purpose: To quantitatively evaluate the reproducibility of patient breathing between the calculated phase from respiratory signal and RPM (real-time position management system, Varian Medical Systems, Palo Alto, CA) within treatment. We developed an independent retrospective verification system (RVS) for gated-radiotherapy using full signal and gating window in RPM system. Methods: RVS was programmed by LabVIEW 2009 with wavelet-based multi-resolution analysis, which is a useful and accurate technique for identifying peaks and valleys of noisy signals. The respiratory signal and real-time calculated phase information from RPM was exported to RVS as a text file. Using this text file, several respiratory parameters were calculated by RVS, and were compared with the generated parameters from RPM. The evaluated parameters included phase-shift, total displacement, residual motion, baseline shift, and so forth. The analysis was conducted for both in-gate and full respiratory signal separately. The analysis report was automatically generated in Excel file format. Eleven patients of abdominal cancer were retrospectively analyzed for the evaluation. Results: The mean phase error of gated signal and full signal between RPM and our software ranged from 1.50% to 3.08% and 1.52% to 3.08%, respectively. Average phase shift was not significant but in-gate phase difference between RVS and RPM was found to be higher than 4% in two cases. At times, real-time phase calculation from RPM caused the beam to be turned on at incorrect time of the breathing cycle when the patient breathing was not regular. The total displacement varied from 0.672 cm to 1.732 cm, which showed patient-specific baseline shift during treatment. Conclusion: The developed software demonstrated competency in analyzing RPM signal and evaluating patient-specific respiratory parameters of radiotherapy. Thus, it can be used as an independent quality assurance tool for RPM phase-based gating treatment.

A CMOS Bidirectional 32-Element Phased-Array Transceiver at 60 GHz With LTCC Antenna

Fully integrated 32-element symmetrical TX/RX 60-GHz RF integrated circuit (RFIC) with built-in self-test is presented. The RF bidirectional power-combining architecture with shared blocks and less than 1-dB millimeter-wave transmit/receive (T/R) switch loss achieves record size and power consumption. The RFIC features an 8-dB noise figure and - 28-dBm IP1 dB in RX mode, 10-dB power gain, and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</i> <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sat</b> of +3.5 dBm per chain in TX mode. Further included are a 2-bit phase shifter, an IF converter to/from 12 GHz, and an integrated frac- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> synthesizer with push-push voltage-controlled oscillator having a-93 dBc@1-MHz phase noise at 48-GHz local oscillator port. A novel high dynamic range phase and power detector is presented with 2° and ±1-dB accuracy over PVT in phase and power. A detailed analysis of both phase quantization and power distribution is presented. Array impairments such as mismatch and coupling were compared for different topologies. The RFIC is packaged on alumina for testing and on low-temperature co-fired ceramic (LTCC) for antenna integration. The 6 × 6 patch antenna on LTCC including four dummies achieves a gain of 19 dBi with scanning of ± 30°. The total root mean square amplitude and phase error of the array is 0.8 dB and 6 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">°</sup> , respectively, resulting in a maximum array beam degradation of 1.4 dB for 2-bit quantization. The RFIC area is 29 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> and it consumes 1.2 W/0.85 W at TX/RX, with a 29-dBm effective isotropic radiated power at -19-dB error vector magnitude.

Complex SAR Image Compression Based on Directional Lifting Wavelet Transform With High Clustering Capability

We propose two synthetic aperture radar (SAR) complex image compression schemes based on DLWT_IQ and DLWT_FFT. DLWT_IQ encodes the real parts and imaginary parts of the images using directional lifting wavelet transform (DLWT) and bit plane encoder (BPE), while DLWT_FFT encodes the real images converted by fast Fourier transform (FFT). Compared with discrete wavelet transform-IQ (DWT_IQ), DLWT_IQ improves the peak signal-to-noise ratio (PSNR) up to 1.28 dB and reduces the mean phase error (MPE) up to 21.74%; and compared with DWT_FFT, DLWT_FFT improves the PSNR up to 1.22 dB and reduces the MPE up to 20.32%. Moreover, the proposed schemes increase the PSNR up to 3.34 dB and decrease the MPE up to 50.43% as compared with the set partitioning in hierarchical trees (SPIHT) algorithm. In addition to this, we observe a novel phenomenon, that is, DLWT with direction prediction achieves a higher clustering capability for complex SAR images than DWT. Then, coding algorithm based on DLWT requires fewer coding bits than DWT for the same number of coding coefficients, and DLWT outperforms DWT in terms of rate-distortion performance even if the K-term nonlinear approximation of DWT is better than that of DLWT.

DESIGN AND IMPLEMENTATION OF AN ULTRA-WIDEBAND SIX-PORT NETWORK

This paper presents a six-port network over an ultra- wideband (UWB) of 2{8GHz. Its key component is the six-port junction, which consists of a Wilkinson power divider and three 3-dB quadrature couplers. This six-port junction is accomplished in a low dielectric constant substrate (Rogers RT/duroid 5880). Multi-section impedance transformation is applied in the power divider, and the quadrature coupler is realized by using two 8.34dB couplers in tandem. An ultra-wideband operation of the six-port junction is verifled by full electromagnetic simulations and measurements. The results show that the designed devices exhibit good performance across 2{8GHz band: the return losses at input ports are higher than 15dB, the insertion losses from input ports to the remaining ports are 7:2dB § 1:7dB, the isolation between two input ports is greater than 20.5dB, and the maximum phase difierence compared with the theoretical behavior between two test ports is 10 - . For the manufactured six-port junction, a six-port phase measurement system and a calibration technique based on support vector regression (SVR) are introduced. Results show that the SVR model can achieve a mean phase error of 1.5274 - .

Direct methods: a paradox with regard to the convergence of random phase trials toward solutions

A frustrating observation, based on an R(min) variance analysis within the `shake and bake' framework of direct methods phasing, is described. The variance of R(min) can on occasion identify large subsets of phases that have a significantly lower mean phase error than the entire direct methods phase set of otherwise unsuccessful phasing trials for which the overall phase error occasionally dips below 75 or 80°. This is the first time, other than for a handful of Σ1 phase indications in optimal situations, that a priori phase estimates have been attained for large numbers of E values, prior to solving the structure. Although the a priori variance of R(min) is a useful tool for identifying such phases, the a posteriori phase refinement shifts indicated by its minimum often prevent a successful convergence to the solution. Similar efforts to encourage solution convergences in the realm of real space have also been discouraging.

Biochemical and Structural Analysis of Bacterial O-antigen Chain Length Regulator Proteins Reveals a Conserved Quaternary Structure

Lipopolysaccharide (LPS) is a major component of the Gram-negative outer membrane and is an important virulence determinant. The O-antigen polysaccharide of the LPS molecule provides protection from host defenses, and the length of O-antigen chains plays a pivotal role. In the Wzy-dependent O-antigen biosynthesis pathway, the integral inner membrane protein Wzz determines the O-antigen chain length. How these proteins function is currently unknown, but the hypothesis includes activities such as a "molecular ruler" or a "molecular stopwatch," and other possibilities may exist. Wzz homologs are membrane proteins with two transmembrane helices that flank a large periplasmic domain. Recent x-ray crystallographic studies of the periplasmic portions of Wzz proteins found multiple oligomeric forms, with quaternary structures favoring the "molecular ruler" interpretation. Here, we have studied full-length Wzz proteins with the transmembrane portions embedded in lipid membranes. Using electron microscopy and image analysis we find a unique hexameric state rather than differing oligomeric forms. The data suggest that in vivo Wzz proteins determine O-antigen chain length via subtle structure-function relationships at the level of primary, secondary, or tertiary structure within the context of a hexameric complex.

Convergence study of a Schrödinger-equation algorithm and structure-factor determination from the wavefunction

The algorithm [Bethanis, Tzamalis, Hountas & Tsoucaris (2002). Acta Cryst. A58, 265-269] which reformulates the quantum-mechanical problem of solving a Schrödinger (S) equation in a crystallographic context has been upgraded and tested for many aspects of convergence. The upgraded algorithm in reciprocal space aims at determining a wavefunction Phi(H) such that (a) Phi(H) fulfils the S equation within certain precision and (b) Phi(H) minimizes by least squares the differences between the calculated structure factors from the wavefunction and the observed ones. Calculations have been made with three molecules (11, 41 and 110 non-H atoms in the asymmetric unit) for different numbers of initially given phases. Three main questions have been addressed: (I) Does the iterative calculation of the wavefunction converge? (II) Do the calculated wavefunctions converge to a unique set of Phi(H) values independent of the initial random set of Phi(H)? (III) Is the calculated Phi(H) set a good approximation of a wavefunction able to produce within certain errors the correct values of the phases of the structure factors? Concerning questions (I) and (II), our results give a strong hint about fast convergence to a unique wavefunction independent of the arbitrary starting wavefunction. This is an essential prerequisite for practical applications. For question (III) in the case closer to the ab initio situation, the final mean phase error, respectively, for the three structures is 3, 26 and 28 degrees. The combination of (a) and (b) in the upgraded algorithm has been proved crucial especially for the results concerning the larger structures.

A numerical study of tidal asymmetry in Okatee Creek, South Carolina

The Okatee River, South Carolina is characterized by a narrow tidal channel and an extensive area of intertidal salt marshes. Current measurements in the upstream portion Okatee Creek show that tidal flow features an asymmetric pattern: ebb current is stronger than flood current. The ebb dominance is mainly caused by deformation of the dominant astronomical tidal constituent M 2. An unstructured grid, finite volume coastal ocean model (FVCOM) with wet-dry point treatment method is applied to examine physical mechanisms of M 4 overtide generation. Model experiments show that mean absolute amplitude and phase errors are 3.1 cm and 1.7 ° for M 2 elevation, 2.4 cm s −1 and 0.8 ° for M 2 current major axis, 2.1 cm and 1.8 ° for M 4 elevation, and 2.1 cm s −1 and 24.6 ° for M 4 current major axis. The overall pattern of tidal asymmetry is qualitatively reproduced. Various sensitivity experiments suggest that the generation of M 4 overtide is a result of nonlinear interaction of tidal currents with irregular creek geometry and bottom topography. Consistent with the classical view, the large volume of intertidal water storage is the major reason for ebb dominance in the creek. However, the zero-inertia assumption (i.e., negligible advective terms) is probably not valid for the entire tidal cycle. Besides the pressure gradient force and the bottom friction force, terms related to lateral shear of the along-estuary velocity (i.e., advective inertia and horizontal eddy viscosity) may also contribute in horizontal momentum balance. Exclusion of the flooding-draining processes over the intertidal zone will severely underestimate tidal currents in the river channel and make the tidal asymmetry less prominent.

Structure determination of theO-methyltransferase NovP using the `free lunch algorithm' as implemented inSHELXE

NovP is an S-adenosyl-L-methionine-dependent O-methyltransferase from Streptomyces spheroides (subunit MW = 29 967 Da). Recombinant N-terminally His-tagged NovP crystallizes in space group P2, with approximate unit-cell parameters a = 51.81, b = 46.04, c = 61.22 A, beta = 105.0 degrees , giving a solvent content of 44% for a single copy of the His-tagged protomer per asymmetric unit. Native synchrotron data to a resolution of 1.35 A were combined with three other native data sets collected at lower resolution (both in-house and at the synchrotron) for the sake of completeness and better scaling. Data to 2.45 A resolution were subsequently recorded in-house from a single mercury derivative. Three partial mercury sites could be located with SHELXD, but the resulting phases had a mean error of about 81 degrees and in our hands did not yield an interpretable map using standard automated software. Nevertheless, the structure of NovP could be solved by first tracing a small part of the structure by hand and then extrapolating within and beyond the experimental resolution limit using the ;free lunch algorithm' in SHELXE. The resulting phases have a mean phase error of 17 degrees relative to a refined model.

Advances in thefree lunchmethod

The most critical limit of macromolecular crystallography, the experimental data resolution, is partially `tricked' by the `free lunchmethod' (non-measured reflection extrapolation). The best electron density map available when only observed data are used may be employed to extrapolate moduli and phases of unobserved reflections behind and beyond the experimental resolution limit. The method is able to reduce the mean phase error of the observed reflections and to produce a more interpretable (in terms of a molecular model) electron density map. The main features of thefree lunchmethod have been studied and its performance has been enhanced; it is beneficial even if data resolution is about 2 Å. Furthermore, the technique has been parameterized so that it may be routinely used by other phasing programs.