Line Length Research Articles

Pilot protection based on the quasi-directional element of LCL-tuned half-wavelength transmission line

To create HWTL characteristics, the electrical distance of AC transmission lines is compensated to half the power frequency wavelength by utilizing tuned circuits. The LCL-tuned circuit exhibits low-pass filtering characteristics, blocking the transmission of high-frequency signals. Measurement devices were installed on both sides of the tuned circuit to assess its filtering characteristics. Based on these characteristics and by employing wavelet transformation to extract the high-frequency energy of the voltage signal on both sides of the tuned circuit as the directional protection criterion, a quasi-directional element was developed. It was determined that, if the high-frequency wavelet energy ratio exceeds one, the fault occurs in the forward direction of the tuned circuit, and if the ratio is less than one, the fault occurs in the reverse direction. Consequently, a pilot protection algorithm was formulated. The directional protection element was integrated with the tuned circuit differential protection to establish the LCL-tuned half-wavelength transmission line pilot protection scheme. This scheme mitigates the need for extensive data synchronization between both sides, and numerous simulations have demonstrated its effectiveness throughout the entire line length, regardless of transition resistance, fault type, noise and outgoing line.

Genetic Algorithm Based Path Planning for Seawater Depth Data Measurement in Real Scenarios

In this paper, firstly, the movement direction of the measuring ship is clarified, and according to the requirements of factors such as the range of overlap rate is controlled at 10% to 20% and the sea area is completely covered, the optimization equation system is derived, and the objective function is derived through the requirements, and the optimal solution can be derived from the two associations as the 34 measuring lines and the total length of 68 nautical miles of the shortest measuring lines. Using genetic algorithm to examine the real scene of seawater depth data measurement path planning, the length of the measurement line and coverage as an assessment index of the algorithm's subsequent optimization of the object of choice. Through the simulation of genetic mutation, crossover and selection operations, the total length of the shortest survey line is 21.5261 nautical miles, the percentage of missed sea area is 1.6%, and the overlap rate is 13.12% after the iterative solution of the genetic algorithm.

Catenary Mooring Length Control for Motion Mitigation of Semi-Submersible Floating Wind Turbines

Besides improving the generator torque and blade pitch controller, incorporating additional control actuations, such as a vibration absorber and active ballast, into the floating offshore wind turbine (FOWT) system is also promising for the motion mitigation of FOWTs. This work aims to study the catenary mooring length re-configuration effect on the dynamic behaviours of semi-submersible FOWTs. The mooring length re-configuration mentioned here is achieved by altering the mooring length with winches mounted on the floating platform, which is in a period of minutes to hours, so that the mooring tensions could be adjusted to reduce the aerodynamic load induced platform mean pitch. Control designs for both single mooring line and multiple mooring lines have been described and studied comparatively. In order to assess the motion mitigation performance of the proposed mooring line length re-configuration methods, fully coupled numerical simulations under different environmental cases have been conducted. Results indicate that the catenary mooring length re-configuration is able to reduce the platform pitch motion by up to 15.8% under rated condition, while careful attention must be paid to the scenarios where the catenary moorings become taut, which may lead to large load variations.

Identification of a novel marker and its associated laccase gene for regulating ear length in tropical and subtropical maize lines

Key messageThis study revealed the identification of a novel gene, Zm00001d042906, that regulates maize ear length by modulating lignin synthesis and reported a molecular marker for selecting maize lines with elongated ears.Maize ear length has garnered considerable attention due to its high correlation with yield. In this study, six maize inbred lines of significant importance in maize breeding were used as parents. The temperate maize inbred line Ye107, characterized by a short ear, was crossed with five tropical or subtropical inbred lines featuring longer ears, creating a multi-parent population displaying significant variations in ear length. Through genome-wide association studies and mutation analysis, the A/G variation at SNP_183573532 on chromosome 3 was identified as an effective site for discriminating long-ear maize. Furthermore, the associated gene Zm00001d042906 was found to correlate with maize ear length. Zm00001d042906 was functionally annotated as a laccase (Lac4), which showed activity and influenced lignin synthesis in the midsection cells of the cob, thereby regulating maize ear length. This study further reports a novel molecular marker and a new gene that can assist maize breeding programs in selecting varieties with elongated ears.

An impedance transformer for UHF RFID and WiFi cross‐technology communication‐based tourism crowd counting

AbstractThis letter proposes a novel cross‐shaped structure‐based parallel coupled line transformer and its application to tag antenna for 920‐MHz radio frequency identification (RFID) and 5‐GHz WiFi Cross‐Technology Communication (CTC). This transformer can be tuned by some lumped capacitors and the equivalent transmission line length for high order harmonic matching. The WiFi is applicable for tourism crowd counting and its counting accuracy may be increased with an additional number of the virtual WiFi Access Points contributed by 5‐GHz resonance of said tags attached with touristic metallic objects. To study the 5‐GHz resonance of these tags the tag antenna is a square patch with a rectangular slot built with 3D acrylonitrile butadiene styrene printing material. The working frequency of the antenna is around 920 MHz, which can achieve a gain of 5.4 dBi and there is also a resonance at 5.6 GHz with a gain of −6.7 dBi. When the capacitor is tuned, the 5‐GHz band of WiFi is varied from 5.2 to 5.6 GHz applicable to emerging WiFi 5 and 6 CTC applications. It is anticipated that the prototype tag provides a flexible tourism crowd counting solution using CTC in the future.

PERANCANGAN JARINGAN DISTRIBUSI UNTUK PLTS TERAPUNG DAN PLTMH DI BENDUNGAN SIDAN

Blahkiuh Feeder is a 20 kV radial distribution network spanning 78.65 kms, which is the longest network in the Mengwi Network Unit. The length of the distribution lines also results in relatively high power losses. Therefore, the installation of distributed generation (DG) utilizing the potential of solar photovoltaic (PV) and micro-hydro power plants (MHP) available at the Sidan Dam has the potential to improve voltage drop and power loss values on the Blahkiuh Feeder. This research was conducted to analyze voltage and power losses due to DG installation at the Sidan Dam, with power flow simulation during peak daytime load at 14:00 and peak nighttime load at 19:00. Simulation results indicate that when interconnected with the daytime peak load at 14:00, DG interconnection results in a decrease in power loss values by 0,8% or 64 kW, and interconnection with the nighttime peak load at 19:00 also leads to a decrease in power loss values by 0.61% or 55 kW. Distributed Generation interconnection on the Blahkiuh Feeder also leads to improvements in voltage values, where interconnection during daytime at 14:00 results in voltage improvement at 41 busbars units under undervoltage condition, and interconnection during night time at 19:00 leads to voltage improvement at only 34 busbars units undervoltage condition out of a total of 50 undervoltage busbars.

Survey of Magnetic Field Parameters Associated with Large Solar Flares

Until now, how the magnetic fields in M/X-class flaring active regions (ARs) differ from C-class flaring ARs remains unclear. Here, we calculate the key magnetic field parameters within the area of high photospheric free energy density (HED region) for 323 ARs (217 C- and 106 M/X-flaring ARs), including total photospheric free magnetic energy density E free, total unsigned magnetic flux ΦHED, mean unsigned current helicity h c , length of the polarity inversion lines L PIL with a steep horizontal magnetic gradient, etc., and compare these with flare/coronal mass ejection (CME) properties. We first show the quantitative relations among the flare intensity, the eruptive character, and ΦHED. We reveal that ΦHED is a measure for the GOES flux upper limit of the flares in a given region. For a given ΦHED, there exists the lower limit of F SXR for eruptive flares. This means that only the relatively strong flares with the large fraction of energy release compared to the total free energy are likely to generate a CME. We also find that the combinations of E free–L PIL and E free–h c present a good ability to distinguish between C-class and M/X-class flaring ARs. Using determined critical values of E free and L PIL, one predicts correctly 93 out of 106 M/X-class flaring ARs and 159 out of 217 C-class flaring ARs. The large L PIL or h c for M/X-class flaring ARs probably implies the presence of a compact current with twisted magnetic fields winding about it.

Analysis of Bridge Dynamics and Response Characteristics Under The Influence of Axle Coupling Vibration

To ensure the safety and stability of high-speed rail lines and reduce external interference, it is essential to build a large number of elevated bridges. These elevated bridges account for a considerable proportion of the total length of high-speed rail lines. However, when high-speed rail lines pass through earthquake prone areas, the likelihood of earthquakes occurring when trains pass through bridges increases significantly. Therefore, it is necessary to study the dynamic response of bridge structures under earthquake action to ensure the safety of bridges during train operation and operation. The optimization scheme proposed in this article has undergone moderate impact tests, and the results show that the maximum lateral displacement of the bridge can reach 124 mm, while the maximum vertical acceleration is 5.16 m/s2, Exceeded the safety limit of 0.35 g. Through the analysis of train derailment coefficient, wheel load reduction rate, lateral sway force, lateral and vertical acceleration, and Spelling comfort index, we have come to the conclusion that bridges can ensure the safety of train operation in the absence of earthquakes and small earthquakes, and can also maintain certain stability under medium and large earthquakes. These research results have important guiding significance for the design and construction of high-speed rail lines. By optimizing the bridge structure and adopting relevant technical measures, the seismic disaster resistance of high-speed rail lines can be further improved, ensuring the safety and comfort of passengers during travel. At the same time, these research results also provide useful reference and inspiration for the construction and improvement of future high-speed rail lines.

A Telegrapher’s equations-based implicit finite difference solution for fault location with current transformer saturation

This paper introduces a fault location method based on time analysis, utilizing synchronized data collected from both ends of the faulted line. The data is obtained either from Common Format for Transient Data Exchange (COMTRADE) files or Sampled Measured Value (SMV) of the IEC-61850 protocol. The method proposed in this study employs the implicit finite difference solution to the Telegrapher’s equations. In certain fault scenarios, such as when one or both transformers experience saturation, a narrow time window of data can be utilized to accurately pinpoint the fault location. The implicit solution method is unconditionally stable and therefore decouples the choice of the line discretization step from the sampling time interval, which is commonly required to maintain numerical stability of the explicit strategies for fault location. Furthermore, the numerical stability of the implicit process allows for devising a systematic search procedure that improves the accuracy of the calculated fault location, regardless of the transmission line length. By conducting numerical comparisons with an explicit time-domain fault locator and recent frequency-domain algorithms, the superiority of the proposed approach becomes evident. The results highlight the significant improvements achieved through the utilization of this method. Specifically, the results demonstrate that Telegrapher’s Equations implicit finite difference solution maintains accuracy under current transformer saturation, as it can locate the fault using data from a brief interval where the current transformer is not saturated.

Methodological Foundations of Film Speech Analysis Using Corpora: Technical, Social, and Cultural-National Aspects

The aim of this study is to describe the possibilities and limitations of the corpus approach to the analysis of film subtitles, taking into account their technical, social, and culturalnational features. It offers a review of existing film content corpora accompanied by their critical interpretation, firstly from the perspective of subtitle quality as empirical data for linguistic research, and secondly from the perspective of corpus quality as an environment for quantitative analysis of empirical material. Furthermore, based on established subtitling practices, the author proposes her own viewpoint on subtitles as material for studying film speech, considering technical (line length, screen size adaptation), social (subtitles for the deaf and hard of hearing), and cultural-national (subtitling countries vs dubbing countries) aspects of subtitling in different languages and countries. In the course of the work, it was found that the largest number of subtitles available in open repositories are translated equivalents of cinema speech. It is noted that subtitling is preferred in the USA, UK, India, China, and Japan. The features of subtitling in countries such as Serbia, Finland, and Russia are described. The author concludes that these features are important for the quality of linguistic research on the basis of translated movie speech represented by subtitles.

Abstract 5650: RNA regulatory disruption by 3’-dATP: A novel approach to inhibit ribosome biogenesis in cancer

Abstract Background: Ribosomes are a complex ensemble of ribosomal RNA and proteins. As the site where genetic information is translated to protein, they have a key role in cell survival, growth and proliferation. Ribosome biogenesis (RiBi), the process of creating ribosomes, is a complex function governed by precise checkpoints and surveillance mechanisms which may become dysregulated in cancer leading to tumor growth and therapeutic resistance. Ribosome-targeted therapy could provide a promising treatment for cancer. NUC-7738 (3'-deoxyadenosine [3’-dA] which is phosphorylated and protected with a phosphoramidate moiety attached at the 5’-position) generates sustained intracellular levels of 3’-dATP, a molecule that profoundly influences RNA regulatory processes, including poly(A) tail length, leading to alternative polyadenylation (APA) and splicing, resulting in impaired cellular responses. NUC-7738 is currently being investigated in combination with pembrolizumab in patients with advanced melanoma in the Phase 2 part of the clinical study (NCT03829254). Here, we investigate the impact of 3’-dATP on RNA regulation and RiBi utilizing a novel bioinformatic pipeline. Material and Methods: RNA was extracted from melanoma and renal carcinoma cell lines treated with NUC-7738 for 24h and paired biopsies (pre and post treatment) from patients treated with NUC-7738 + pembrolizumab. Sequencing libraries used for long-read PCR-cDNA sequencing were generated. Gene-level expression was quantified using Salmon DeSeq2. In addition to gene expression, poly(A) tail length, APA and isoform switch were analyzed. Protein expression was determined using JESS Western analysis. Multiplexed analysis of protein localization and expression in tissue was carried out using an in-house immunofluorescence protocol. Results: NUC-7738 caused a global reduction in poly(A) tail length in cell lines and patient biopsies that was most pronounced in the poly(A) tail exosome targeting (PAXT) long non-coding RNA (lncRNA) transcripts, including SNHG19, 5’TOP and YAE1, all of which play a role in RiBi. PAXT lncRNAs such as SNHG3 and SNHG19 increased in abundance. Ribosomal subunit proteins such as RPS3, RPS6, RPL17 decreased in expression. Expression of YAE1, a regulator of RiBi, also decreased. Distinct APA usage of various transcripts was observed in cell lines and patient biopsies. Conclusion: Through the development of a novel bioinformatic pipeline we have been able to demonstrate that NUC-7738 disrupts RNA regulation, leading to perturbed RiBi. Targeting RiBi provides a promising approach to treating cancers Citation Format: Mustafa Elshani, Ying Zhang, In Hwa Um, Ruth Plummer, Sarah P. Blagden, Stefan N. Symeonides, Natalie Cook, T.R. Jeffry Evans, Alison L. Dickson, David J. Harrison. RNA regulatory disruption by 3’-dATP: A novel approach to inhibit ribosome biogenesis in cancer [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2024; Part 1 (Regular Abstracts); 2024 Apr 5-10; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2024;84(6_Suppl):Abstract nr 5650.

Результаты сравнения длин линий на базисе пространственном эталонном СГУГиТ

The results of line lengths comparison on the spatial reference basis (SRB) of SGUGiT, carried out according to the program in all combinations measurements in the forward direction from point BI01 to point BI10 in spring and summer of 2021 and 2023 using total station Leica TM30, as well as, in the same seasons of 2023 done by laser tracker Leica AT403 are given. Based on the analysis of multiple measurements of each section of the basis (at least 30 ones), the standard deviation and uncertainty were calculated. Meanwhile, at the extreme points of the base section, meteorological parameters (temperature, pressure and relative humidity) were recorded by two independent instruments, which were then entered immediately when metering with a Leica TM 30 electronic total station. In the case of the Leica AT403 laser tracker, they were automatically taken into account in specialized software management and processing of Spatial Analyzer measurement data. Due to the research results, it was found out that the expanded uncertainty in measuring the lengths of the basic lines in the range from 12 to 192 m on the WPT using a Leica AT403 laser tracker and a Leica TM30 electronic total station, taking into account the accepted errors that affect the final result, is no more than 1,4 mm, and the maximum contribution to the mistake in determining line lengths is made by the standard uncertainty estimated by type B. In addition, seasonal fluctuations in the position of individual basis points are observed

Force-sensing treadmill gait analysis system can detect gait abnormalities in haemophilia patients without arthropathy.

Joint damage in patients with haemophilia (PwH) is commonly assessed by imaging, but few reports have described how structural changes in joints, for example, haemophilic arthropathy (HA)-affect gait ability. We evaluated gait function among PwH with HA, PwH without HA, and people without haemophilia (non-PwH) using a Zebris FDM-T treadmill (FDM-T), an easy-to-use gait assessment instrument with a force sensor matrix. The following gait parameters were collected: centre of pressure trajectory intersection (COPi) anterior/posterior variability, COPi lateral variability, COPi anterior/posterior symmetry, COPi lateral symmetry, single-limb support line (SLSL) length, and SLSL variability. Participants walked at their typical gait speed. The physical function of the PwH was assessed by the Hemophilia Joint Health Score (HJHS). Parameters were compared among the three groups. Twelve PwH with HA, 28 PwH without HA, and 12 non-PwH were enrolled. Gait speed significantly differed between groups (non-PwH, 3.1±0.7; PwH without HA, 2.0±0.7; PwH with HA; 1.5±0.4). The COPi anterior/posterior variability, COPi lateral variability, SLSL length, and SLSL variability were greater in the PwH groups than in the non-PwH group. The COPi lateral symmetry differed between PwH with HA and the other groups. The HJHS was not correlated with gait parameters among PwH with HA. Gait parameters and speed were abnormal in both PwH with HA and PwH without HA. The FDM-T can be used to identify early stages of physical dysfunction that cannot be detected by conventional functional assessments such as the HJHS.

A New Formula for Estimating Insertion Length of Umbilical Catheters in Neonates: An Observational Study

Objective: Current formulae used by clinicians to estimate the insertion length of umbilical catheters are inaccurate. We aimed to derive a new model that could improve accuracy in estimating the insertion length of umbilical catheters. Study design: This was a multi-centre prospective observational study of neonates admitted to neonatal units and needing umbilical line(s) inserted for clinical reasons. Demographic data, catheter-related measurements and a new external length measurement—sternal notch to the umbilicus, were collected at three tertiary-level neonatal units in South Wales, UK. Generalised linear models were used to estimate the fit of the external length, birthweight, gestation and head circumference with catheter length and to derive a formula. The best fit was estimated by comparing r 2 values for each equation. Results: Data from 113 infants for each venous and arterial line were analysed for the new mathematical formulae. For both umbilical arterial catheterisation [[Formula: see text] and umbilical venous catheter (UVC) [[Formula: see text]], a quadratic model based on birthweight was found to have the best fit for predicting the insertion length of the catheters. However, the overall fit for UVCs was poorer for all explanatory variables ( y = estimated insertion length of the umbilical catheter in cm, x = birthweight in kg). Conclusion: Our prospective multi-centre observational study identified a quadratic model based on birthweight as the best fit for estimating the insertion length of umbilical lines in neonates. This is a new finding and further development on earlier birthweight-based linear models.

Reduced influence of perceptual context in mild traumatic brain injury is not an illusion.

Perceptual grouping is impaired following mild traumatic brain injury (mTBI). This may affect visual size perception, a process influenced by perceptual grouping abilities. We conducted two experiments to evaluate visual size perception in people with self-reported history of mTBI, using two different size-contrast illusions: the Ebbinghaus Illusion (Experiment 1) and the Müller-Lyer illusion (Experiment 2). In Experiment 1, individuals with mTBI and healthy controls were asked to compare the size of two target circles that were either the same size or different sizes. The target circles appeared by themselves (no-context condition), or were surrounded by smaller or larger circles (context condition). Similar levels of accuracy were evident between the groups in the no-context condition. However, size judgements by mTBI participants were more accurate in the context condition, suggesting that they processed the target circles separately from the surrounding circles. In Experiment 2, individuals with mTBI and healthy controls judged the length of parallel lines that appeared with arrowheads (context condition) or without arrowheads (no context condition). Consistent with Experiment 1, size judgements by mTBI participants were more accurate than size judgements by control participants in the context condition. These findings suggest that mTBI influences size perception by impairing perceptual grouping of visual stimuli in near proximity.

Design of High-Gain Antenna Arrays for Terahertz Applications.

A terahertz band (0.1-10 THz) has the characteristics of rich spectrum resources, high transmission speed, strong penetration, and clear directionality. However, the terahertz signal will suffer serious attenuation and absorption during transmission. Therefore, a terahertz antenna with high gain, high efficiency, and wide bandwidth is an indispensable key component of terahertz wireless systems and has become a research hotspot in the field of antennas. In this paper, a high-gain broadband antenna is presented for terahertz applications. The antenna is a three-layer structure, fed by a grounded coplanar waveguide (GCPW), using polytetrafluoroethylene (PTFE) material as the dielectric substrate, and the metal through-hole of the dielectric substrate forms a substrate-integrated waveguide (SIW) structure. The metal fence structure is introduced to reduce the coupling effect between the radiation patches and increase the radiation bandwidth and gain. The center frequency is 0.6366 THz, the operating bandwidth is 0.61-0.68 THz, the minimum value of the voltage standing wave ratio (VSWR) is 1.00158, and the peak gain is 13.14 dBi. In addition, the performance of the designed antenna with a different isolation structure, the length of the connection line, the height of the substrate, the radius of the through-hole, and the thickness of the patch is also studied.

FCC-Zr phase transformation-induced defect substructure in Zr2Si precipitates equilibrated in Si-modified Zircaloy-4

This work investigates the atomic scale substructure of interfaces in Zr2Si secondary phase precipitates formed by the stresses associated with the α-Zr (HCP) to γ-Zr (FCC) phase transformation and thermal effects in an experimental Si-modified Zircaloy-4 by means of transmission electron microscopy and CSL/DSCL (coincident site lattice/displacement shift complete lattice) models. Analysis of a high-angle twin interface reveals their characteristic principal primary Δg vectors, a typical feature of the singular interfaces, and the sessile twinning disconnections. The step height and length of the interfacial dislocation line, with the Burgers vector parallel to the habit plane, are analysed using the DSCL model. In the second case, a low-angle interface of mixed tilt-twist character is studied and facets of constant length along the densest-packed planes and ledges of inconstant height, a common feature of vicinal interfaces, are identified.

Effects of dough sheets resting on textural properties of long‐life noodles via moisture migration and gluten network development

SummaryNoodles are a popular staple food for many Asian populations. This study aimed to explore the effects of different resting temperatures (15, 25, 35, 45 °C) and humidity (65%, 75%, 85%, 95%) on the quality of long‐life noodles (LL noodles) by considering the moisture migration and microstructure of gluten network in dough sheets. According to results, at resting conditions (25 °C and 95% relative humidity), the dough sheet exhibited a shorter transverse relaxation time of tightly bound water (T21) and higher relative content (A21), which facilitated a tight combination between other components and water molecules. Additionally, a dense and uniform distribution of gluten network was achieved at 25 °C and 95%, due to a reduction in average length and width of gluten network lines, as well as to increased branching rate. Therefore, LL noodles were endowed with a lower cooking loss rate and higher water absorption rate, and the texture properties including chewiness, hardness, smoothness and elasticity were at optimal level. The present work demonstrated the possibility of using a resting at 25 °C and 95% humidity to enhance the uniformity of gluten network and texture of dough sheets and significantly improved the texture properties of LL noodles.

Solid solution strengthening of the body-centered cubic refractory complex concentrated alloy, MoNbTaW

In this manuscript, experimental yield stress data as a function of temperature of the body-centered cubic refractory complex concentrated alloy MoNbTaW are analyzed using two solid solution strengthening models: the Rao-Suzuki model (screw strengthening) and the Maresca-Curtin model (edge strengthening). It is shown that the Rao-Suzuki model results are in reasonable agreement with the experimental yield data whereas the Maresca-Curtin model underpredicts the strengthening. Similarly, molecular dynamics data on the critical stress to move screw and edge dislocations in MoNbTaW are analyzed using the Rao-Suzuki and the Maresca-Curtin models, respectively. It is shown that the molecular dynamics edge mobility results are in reasonable agreement with the Maresca-Curtin model whereas the molecular dynamics simulated data on the critical stress to move screw dislocations in MoNbTaW severely overpredicts the Rao-Suzuki model. This is argued to be a result of the very small dislocation line lengths used in the molecular dynamics simulations, ∼150A.

Textual Criticism in the Gaps

Abstract This article concerns the likelihoods of competing textual reconstructions in the Chester Beatty Papyrus 𝔓⁴⁶ based on the available space in its lacunose lines. To quantify these relative probabilities, the author uses statistical models of line lengths in 𝔓⁴⁶ and a recently described technique for calculating the likelihood of a reconstructed lacunose text. He first demonstrates the power and versatility of this approach with examples in Gal 4:17 and 3:1. He then revisits two more contested textual reconstructions proposed for 𝔓⁴⁶: the absence of τῷ θεῷ in Heb 11:4, suggested by G.D. Kilpatrick in 1941, and the absence of σὺν ἐπισκόποις καὶ διακόνοις in Phil 1:1, suggested by T.C. Skeat in 1995. He shows that Kilpatrick’s proposed shorter reading in 𝔓⁴⁶ is six times more likely than the longer reading in Heb 11:4, while the evidence is not decisive between the readings in Phil 1:1.