Power Formula Research Articles

Accuracy of thick and thin intraocular lens power formulas using paraxial vergence calculation.

To compare the prediction errors of several thick IOL formulas to a thin lens approach using variations of the same paraxial vergence calculation formula. Department of Ophthalmology, Randers Regional Hospital, Denmark. Prospective, non-interventional study. We prospectively and consecutively performed optical low coherence reflectometry biometry in 132 eyes with subsequent phacoemulcification and insertion of the same aspherical IOL model. Clinical refraction was performed two months postoperatively. We retrospectively used the same paraxial vergence formula and varied only the methods for calculating the postoperative IOL position, thickness, and curvatures to construct four formulas: Næser I formula based on thick lens calculation using the manufacturer´s cutting card information; Næser II formula based on thick lens calculation using calculated IOL data from open sources; Næser III formula based on thick lens calculation and a fixed IOL thickness of 0.62 mm; Næser IV formula based on thin lens calculation with fixed IOL position 0.31 mm anterior to the postoperative capsule. Each formula was optimized separately, hereby assuring a mean error of zero. The prediction error (PE) was defined as the difference between the measured and predicted spherical equivalent refraction. Mean absolute error amounted to 0.30 (±0.26) D for all four formulas with no statistically significant difference. PE averaged zero for short, normal, and long eyes. The additional optical information provided by thick IOL calculations appears insignificant compared to other sources of error, related to the accuracy of IOL manufacturing, natural lens refractive index, and postoperative refraction.

Post-Newtonian Effects in Compact Binaries with a Dark Matter Spike: A Lagrangian Approach

We apply the Lagrangian method to study the post-Newtonian evolution of a compact binary system with environmental effects, including a dark matter spike, and obtain the resulting gravitational wave emission. This formalism allows one to incorporate post-Newtonian effects up to any desired known order, as well as any other environmental effect around the binary, as long as their dissipation power or force formulae are known. In particular, in this work, we employ this method to study a black hole–black hole binary system of mass ratio 105 by including post-Newtonian effects of order 1PN and 2.5PN, as well as the effect of relativistic dynamical friction. We obtain the modified orbits and the corresponding modified gravitational waveform. Finally, we contrast these modifications against the LISA sensitivity curve in frequency space and show that this observatory can detect the associated signals.

A remote monitoring method for gateway electric energy meters based on electric energy, voltage and current conservation decomposition

Abstract A remote monitoring technique for gateway electricity meters is introduced that leverages conservation principles of electric energy, voltage, and current. It aims to tackle issues related to errors in electric energy meters and transformers that are challenging to distinguish, as well as the high costs associated with on-site testing. The ridge regression is used to solve the formulas for bus power and current conservation to obtain gateway metering points’ error and current loops’ error. The voltage loop error is determined through an averaging method, which is then used to calculate the error in electric energy meters. The voltage consistency method is used to synchronize the time bias between gateway electricity meters, ensuring accurate calculations. The analysis results indicate that the proposed method effectively monitors the operating status of gateway electric energy meters and offers greater accuracy compared to benchmarks. This method can timely discover suspected inaccurate electricity meters, aiding in their maintenance and efficient operation.

A New Intraocular Lens Power Formula Integrating an Artificial Intelligence-Powered Estimation for Effective Lens Position Based on Chinese Eyes.

To develop and evaluate a new intraocular lens (IOL) formula based on Chinese eyes. A training dataset of 709 eyes undergoing uneventful cataract surgery was used to train the algorithm for effective lens position estimation. The algorithm was then integrated with Gaussian optics to develop the new IOL formula (Jin-AI). From the same center, 177 eyes served as an internal test dataset. An independent dataset of 557 eyes served as an external test dataset. The standard deviation (SD) of prediction errors was compared among the Jin-AI formula, traditional third-generation formulas (SRK/T, Holladay 1, Hoffer Q), and newer generation formulas (Kane, Barrett Universal II [BUII], Hill-radial basis function [RBF] 3.0, and PEARL-DGS). In the internal test dataset, the Jin-AI formula showed the lowest SD (0.25 D), followed by the BUII (0.31 D), Kane (0.33 D), and PEARL-DGS (0.33 D) formulas. In the external test dataset, the Jin-AI, Kane, and PEARL-DGS formulas had the lowest SD (0.38 D), followed by the BUII (0.39 D), Hill-RBF 3.0 (0.39 D), SRK/T (0.45 D), Holladay 1 (0.48 D), and Hoffer Q (0.48 D) formulas. The SD of the Jin-AI formula was significantly lower than the third-generation formulas and comparable to the four newer generation formulas. Predictive accuracy of the Jin-AI formula was similar to the newer generation formulas across all axial length, keratometry, and anterior chamber depth ranges. The new formula has exhibited good performance in predicting postoperative refractions. Its overall predictive accuracy was better than the third-generation formulas and comparable to the newer generation ones. The Jin-AI formula could be a reliable alternative for IOL power calculation in Chinese.

Hybrid DC circuit breaker power supply system with load constant voltage self‐balancing design

AbstractPower electronic switches (PES) play a crucial role in transferring and clearing fault currents in hybrid DC circuit breakers. The PES encounters switching transients that require a dependable external power source. Usually, a power supply system utilizes an isolation transformer and many magnetic rings. However, the existence of inconsistent parameters might easily cause an imbalance in load power, which could potentially result in power supply failure for the loads. Therefore, to enhance the reliability of power supply, this study proposes a load constant voltage self‐balancing design approach that utilizes feedback circuits to achieve stability and balance in load voltage. At first, two feedback circuits are shown, and the analytical formulas for load active power and load voltage are derived. Moreover, a parameter design methodology is shown for the equivalent circuit of the magnetic rings in the power supply. Additionally, a power supply system is built with 24 V outputs. In conclusion, this study utilizes simulations and tests to assess the effectiveness of the proposed power supply system by analysing its performance during start‐up, load power‐off, and steady‐state operations.

Monotonic simple shear characteristics of K0 highly over-consolidated and remolded Wenzhou clay

The over consolidated clay is widely distributed in the seabed. Monotonic simple shear tests on K 0 consolidated clays with an over consolidation ratio (OCR) of 1 ∼ 14 were conducted through a multidirectional cyclic simple shear apparatus. The stress–strain relationship, pore pressure evolution, and shear strength variation under different OCRs were revealed, and differences between over and normally consolidated clay were compared. When OCR is below 8, peak values of shear stress and negative excess pore pressure both increase linearly with increasing OCR. However, the peak values tend to stabilize when OCR is above 8. Correspondingly, the occurrences of peak values no longer delay linearly, and the failure line is also shifted towards stronger strengths. An exponential formula is purposed and validated on accordance with numerous experimental data to describe the aforementioned pattern more precisely compared with the traditional power formula. Therefore, shear strengths of over consolidated clays with various OCRs and consolidation pressures can be accurately predicted according to the exponential formula and the shear strength of a normally consolidated sample with a certain consolidation pressure.

Comparison of intraocular lens power formulas for negative-diopter intraocular lens implantation for high myopia.

To compare the accuracy of intraocular lens (IOL) power calculation formulas for myopic eyes requiring negative diopter powered IOLs. Retrospective case series. K… hospital and Y… Hospital, …, …. Sixty-one eyes that underwent phacoemulsification with implantation of a negative power IOL were investigated. The trueness, precision and accuracy of IOL power calculation were assessed for the Barrett Universal II (BUII), EVO 2.0, Haigis, Hoffer QST, Holladay 1 and SRK/T formulas using the Eyetemis online tool. The analysis was performed using 1) the ULIB IOL constants and 2) after constant optimization. With ULIB constants, the Haigis, Holladay 1 and SRK/T resulted in a hyperopic mean prediction error (PE) >1.00 diopter (D), which was significantly different from zero (adjusted p <0.05). The mean PE of the remaining formulas was closer to zero. The absolute PE was significantly higher with the Holladay 1 and SRK/T (adjusted p <0.05) with respect to the remaining formulas. After constant optimization, the outcomes of traditional formulas improved and no statistically significant differences were found among any of the formulas in terms of trueness, precision and accuracy. The percentage of eyes with an absolute PE within 0.50 D was low (<50%) even after constant optimization. With ULIB constants, the BUII, EVO 2.0 and Hoffer QST were more accurate than traditional formulas in eyes with negative-diopter IOLs. The results of IOL power calculation in these eyes remain poor even after constant optimization.

Impact of the Minimization of Standard Deviation Before Zeroization of the Mean Bias on the Performance of IOL Power Formulas.

In cataract surgery, accurate intraocular lens (IOL) power calculations are crucial for optimal postoperative refractive outcomes. This study explores the impact of prioritizing the reduction of the standard deviation (SD) of prediction errors before mean prediction error (PE) adjustment on IOL calculation formula precision and accuracy. We conducted a retrospective analysis of 4885 eyes from 2611 patients, all implanted with the same IOL model, comparing four traditional IOL power calculation formulas: SRK/T, Holladay 1, Haigis, and Hoffer Q. We introduced new constants aiming to minimize the SD of PE (new_const) against traditionally optimized constants (classic_const), using a heteroscedastic statistical method for comparison. Validation of precision improvements used a secondary dataset of 262 eyes from 132 patients. We observed significant reductions in mean absolute error (MAE) across training and test sets for Hoffer Q, Holladay, and Haigis formulas, indicating accuracy enhancements. Optimized constants significantly reduced SDs for Haigis from 0.3255 to 0.3153 and for Hoffer Q from 0.3521 to 0.3387. These optimizations also increased the proportion of eyes achieving PE within ±0.25D. SRK/T showed improved SD from 0.3596 to 0.3585. However, Holladay 1 showed minimal change with no significant improvement. In the test dataset, significant reductions in SD were observed for Haigis and Hoffer Q. Prioritizing SD minimization before adjusting mean PE significantly improves the precision of selected IOL power formulas, enhancing postoperative refractive outcomes. The effectiveness varies among formulas, underscoring the need for formula-specific adjustments. The study presents a novel two-step approach for optimizing IOL power calculations.

Priority-driven harmonic power sharing strategy for interlinking converters based on distributed consensus protocol

This paper investigates the issue of accurate harmonic power sharing in a microgrid clusters connected with interlinking converters. A distributed consensus protocol is developed for controller to adaptively regulate the virtual impedance at harmonic frequencies. Further, a simplified formula of the harmonic apparent power is adopted to reduce the calculation burden. With the proposed methods, harmonic power can be proportionally shared among ILCs and AC sub-grid according to sub-grid priority index,which improves the higher weight sub-grid voltage quality. Thus, the microgrid clusters system flexibility can be enhanced and the knowledge of he line impedance is not required. Finally, the effectiveness of the proposed strategy is verified by hardware-in-the-loop experiments.

A Biomimetic Autophagosomes-Based Nanovaccine Boosts Anticancer Immunity.

Personalized cancer vaccines based on tumor cell lysates offer promise for cancer immunotherapy yet fail to elicit a robust therapeutic effect due to the weak immunogenicity of tumor antigens. Autophagosomes, obtained from pleural effusions and ascites of cancer patients, have been identified as abundant reservoirs of tumor neoantigens that exhibit heightened immunogenicity. However, their potential as personalized cancer vaccines have been constrained by suboptimal lymphatic-targeting performances and challenges in antigen-presenting cell endocytosis. Here,a reinforced biomimetic autophagosome-based (BAPs) nanovaccine generated by precisely amalgamating autophagosome-derived neoantigens and two types of adjuvants capable of targeting lymph nodes is developed to potently elicit antitumor immunity. The redox-responsive BAPs facilitate cytosolic vaccine opening within antigen-presenting cells, thereby exposing adjuvants and antigens to stimulate a strong immune response. BAPs evoke broad-spectrum T-cell responses, culminating in the effective eradication of 71.4% of established tumors. Notably, BAPs vaccination triggers enduring T-cell responses that confer robust protection, with 100% of mice shielded against tumor rechallenge and a significant reduction in tumor incidence by 87.5%. Furthermore, BAPs synergize with checkpoint blockade therapy to inhibit tumor growth in the poorly immunogenic breast cancer model. The biomimetic approach presents a powerful nanovaccine formula with high versatilityfor personalized cancer immunotherapy.

Dose increment in ultrashort particle irradiations via coherent stopping power

We present a relativistic self-consistent theory of the coherent stopping power (CSP) of ultradense charged particle beams propagating in a dense matter. CSP corresponds to a collective inelastic collision which adds to the ordinary stopping power of individual particles. Unlike the latter, which depends only on the particles' energy, CSP depends upon many more parameters such as the total charge of the ensemble and its charge density and shape. This paves the way for a broad variety of novel methods to tailor particle absorption and penetration in a dense matter. CSP losses can be explained both by collective excitations of single or multiple molecules and by the emission of coherent Cherenkov radiation. Here we demonstrate that the former mechanism is more relevant than the latter. We find that the coherent energy absorption of subpicosecond particle bunches in water occurs exciting a broad Debye process in the GHz range and an intermolecular stretching vibration mode in the THz region. We generalize the Bethe-Bloch stopping power formula to coherent effects including self-forces, dielectric screening, and absorption by the dense matter. For the sake of a self-consistent dynamical theory including phase space evolution, we have also generalized the Fermi-Eyges theory of particle diffusion to the presence of forces. Nonlinear dynamics is demonstrated, inducing nonlinear dose release, beam self-focusing, and self-enhancement of coherent losses. Given the advent of ultraintense particle sources and their use for biomedical and other relevant applications, our results may be of paramount importance for contemporary and future developments of science and technology. Published by the American Physical Society 2024

Statistical power and optimal design for randomized controlled trials investigating mediation effects.

Mediation analyses in randomized controlled trials (RCTs) can unpack potential causal pathways between interventions and outcomes and help the iterative improvement of interventions. When designing RCTs investigating these mechanisms, two key considerations are (a) the sample size needed to achieve adequate statistical power and (b) the efficient use of resources. The current study has developed closed-form statistical power formulas for RCTs investigating mediation effects with and without covariates under the Sobel and joint significance tests. The power formulas are functions of sample size, sample allocation between treatment conditions, effect sizes in the treatment-mediator and mediator-outcome paths, and other common parameters (e.g., significance level, one- or two-tailed test). The power formulas allow us to assess how covariates impact the magnitude of mediation effects and statistical power. Accounting for the potential unequal sampling costs between treatment conditions, we have further developed an optimal design framework to identify optimal sample allocations that provide the maximum statistical power under a fixed budget or use the minimum resources to achieve a target power. Illustrations show that the proposed method can identify more efficient and powerful sample allocations than conventional designs with an equal number of individuals in each treatment condition. We have implemented the methods in the R package odr to improve the accessibility of the work. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

The Chronic Progressive Repeated Measures (CPRM) Model for Clinical Trials Comparing Change Over Time in Quantitative Trait Outcomes

Repeated measures analysis is a common analysis plan for clinical trials comparing change over time in quantitative trait outcomes in treatment versus control. Mixed model for repeated measures (MMRM) assuming an unstructured covariance of repeated measures is the default statistical analysis plan, with alternative covariance structures specified in the event that the MMRM model with unstructured covariance does not converge. We here describe a parsimonious covariance structure for repeated measures analysis that is specifically appropriate for longitudinal repeated measures of chronic progressive conditions. This model has the parsimonious features of the mixed effects model with random slopes and intercepts, but without restricting the repeated measure means to be linear with time. We demonstrate with data from completed trials that this pattern of longitudinal trajectories spreading apart over time is typical of Alzheimer’s disease. We further demonstrate that alternative covariance structures typically specified in statistical analysis plans using MMRM perform poorly for chronic progressive conditions, with the compound symmetry model being anticonservative, and the autoregressive model being poorly powered. Finally, we derive power calculation formulas for the chronic progressive repeated measures model that have the advantage of being independent of the design of the pilot studies informing the power calculations. When data follow the pattern of a chronic progressive condition. These power formulas are also appropriate for sizing clinical trials using MMRM analysis with unstructured covariance of repeated measures.

Exploring the Links Between Social Media Addiction, Body Satisfaction, and Subjective Well-Being Among Adolescents

The current study examined Social media addiction, body satisfaction, and subjective well-being among adolescents. For this purpose, the sample for the current study was calculated by the G power formula (F, t, χ2, Z, and exact tests) 300 participants were selected through the convenient sampling technique (139 Boys and 161 Girls), adolescents with the age range of 10-19 from different colleges and universities of Faisalabad. The Co-relational research design was used in the current study. The variables under research were measured using the following scales: The Bergen Social Media Addiction Scale (Andreassen et al., 2016), the Body Shape Questionnaire (Cooper et al., 1987), the Rosenberg Self-Esteem Scale (Rosenberg,1965), the Work &amp; Social Adjustment Scale (Marks et al., 2002), ICP Subjective Well-Being Scale (Diener's, 1984). Using SPSS version 26, descriptive statistics, correlation, and t-tests were used to evaluate the current research hypothesis. Results of the correlation analysis revealed that there is a significant negative relationship between social media addiction and body satisfaction. In contrast, body satisfaction and subjective well-being were significantly positively related, and subjective well-being with body satisfaction showed no ties. The findings will benefit adolescents and management in schools and universities by providing a healthy environment and social skills to reduce social media addiction. Excessive social media use negatively impacts adolescents' body satisfaction and overall well-being. For adolescents, there is a need for educational programs and open communication to promote healthy online habits and to reduce social media's negative effects, with parental support playing a crucial role.

Unwilling the Smartphone Addiction, Fear of Missing Out and Mental Health Issues in Youth

The focus of present is to explore the relationship between smartphone addiction, fear of missing out and mental health issues in youth. Understanding how specific worries of missing out and mental health issues contribute to the development and exacerbation of smartphone addiction can provide valuable insights for prevention strategies. For this purpose, the sample for the current study was calculated by the G power formula (F, t, χ2, z, and exact tests) and 200 participants were selected through convenient sampling. A correlational research design was used. A short smartphone addiction scale (Kwon et al., 2013), fear of missing out (Przybylski et al., 2013) and mental health questionnaire scale (Houston) were used to measure the study variables. Results of the correlation analysis revealed that there is a significant positive relationship between smartphone addiction, fear of missing out and mental health issues in youth. Further results demonstrate that smartphone addiction significantly predicts mental health issues in youth. However, results showed that there are no gender differences in smartphone addiction, Fear of missing out and mental health issues among young adults. The current study findings are beneficial for youth to understand how smartphone addiction is linked to fear of missing out and mental health issues and what steps should be taken to reduce these issues in youth. To conclude, the present research study highlights the need for awareness and intervention strategies to mitigate the adverse effects of Smartphone addiction and FOMO on mental health, emphasizing the importance of digital literacy and balanced technology use among youth.

Accuracy of formulas for intraocular lens power for eyes undergoing descemet stripping automated endothelial keratoplasty and cataract surgery.

To compare accuracy in intraocular lens (IOL) power calculation in eyes undergoing combined cataract and Descemet stripping and automated endothelial keratoplasty (C-DSAEK) surgery of the following formulas: Barrett Universal II, EVO, Haigis, Hoffer Q, Holladay 2, Kane and SRK/T. 72 eyes from 72 patients (38 males, (53%)) with a mean age 68.08 ± 8.69 years (from 44 to 88 years old) underwent combined C-DSAEK were included. The IOL powers to implant were calculated with Barrett Universal II formula targeting -1 D refraction. Preoperative and postoperative data were used to obtain the median of absolute prediction errors (MAE) targeting emmetropia with every tested formula. Means of MAE calculated were +1.45 D for Barrett Universal II, +1.37 D for EVO, +1.48 D for Haigis, +1.38 D for Hoffer Q, +1.37 D for Holladay 2, +1.39 D for Kane and +1.31 D for SRK/T. SRK/T MAE showed major significant (p < 0.01) differences compared to the other formulas. Even if tested formulas are not able to accurately target emmetropia, SRK/T seems to be able to provide closer results in eyes undergoing C-DSAEK.

The automorphism group of finite 2-groups associated to the Macdonald group

We consider the Macdonald group [Formula: see text] and its Sylow 2-subgroup [Formula: see text], where [Formula: see text] and [Formula: see text] is odd. Then [Formula: see text] has order [Formula: see text], and nilpotency class 5 if [Formula: see text] and 3 if [Formula: see text]. We determine the automorphism group of the 2-groups [Formula: see text], [Formula: see text] and [Formula: see text], where [Formula: see text] and [Formula: see text]. Explicit multiplication, power, and commutator formulas for [Formula: see text], [Formula: see text] and [Formula: see text] are given, and used in the calculation of [Formula: see text], [Formula: see text] and [Formula: see text].

Accuracy of intraocular lens power formulas in patients with average keratometry greater than 46 diopters

ObjectiveTo compare the accuracy of Kane, Barrett Universal II, Haigis, and SRK-T formulas in eyes with average keratometry greater than 46 diopters (D). MethodsA retrospective analysis was conducted on 101 eyes of 101 patients with average keratometry greater than 46 D. The absolute prediction error (EA) was obtained for each patient one month after surgery. The mean absolute prediction error (MEA), median absolute prediction error (MedEA) and the percentage of patients with absolute refractive error less than 0.25 D, 0.50 D, and 1.00 D were calculated for each formula analyzed. ResultsThe Kane formula achieved the lowest MEA (0.53 ± 0.43) and the lowest MedEA (0.41), followed by Barrett Universal II (MEA: 0.56 ± 0.42, MedEA: 0.49), SRK-T (MEA: 0.59 ± 0.44, MedEA: 0.54), and Haigis (MEA: 0.77 ± 0.47, MedEA: 0.69), showing a significant difference in the results. It was also observed that the Kane formula was the most accurate, with the highest percentage of patients, with EA less than 0.25 D, 0.50 D, and 1.00 D (30.7%, 54.4%, and 86.1%, respectively), while the Haigis formula was the least accurate (12.9%, 33.7%, and 69.3%, respectively). ConclusionIn eyes with corneas having average keratometry greater than 46 D, the Kane formula proves to be a useful tool in intraocular lens (IOL) power calculation and demonstrates higher precision compared to the Barrett Universal II, SRK-T, and Haigis formulas.

Comparison of keratometry and total corneal power, as measured by an SS-OCT-based optical biometer, for intraocular lens power calculation in Asian eyes.

To investigate whether standard keratometry (K) or total corneal power (TCP) leads to more accurate refractive outcomes for intraocular lens (IOL) power calculation. Public hospital. Retrospective evaluation of a diagnostic test instrument. Preoperatively, all patients underwent optical biometry with Anterion, a swept-source optical coherence tomography device providing both K and TCP. The same IOL model was implanted in all cases. The whole sample was divided into a training dataset, used to optimize the formula constants, and a testing dataset, used to investigate the spherical equivalent prediction error (SEQ-PE) of 8 IOL power formulas. Trueness, precision, and accuracy were evaluated by means of the robust 2-sample t test. Cochran Q test was performed to assess whether the percentage of eyes with an SEQ-PE within each threshold was significantly different; in such an event, the McNemar test was then applied. Both the training and testing datasets included 317 eyes. No significant differences were detected for trueness because of constant optimization. Precision and accuracy were better when K was entered, although a statistically significant difference was observed only with the EVO (precision: P = .02 and accuracy: P = .03) and Haigis ( P < .01 for both precision and accuracy) formulas. No significant differences were observed for the percentage of eyes with an absolute SEQ-PE within any threshold. With most formulas, IOL power calculation is not more accurate when TCP is used instead of K.

Generalized kernel distance covariance in high dimensions: non-null CLTs and power universality

Abstract Distance covariance is a popular dependence measure for two random vectors $X$ and $Y$ of possibly different dimensions and types. Recent years have witnessed concentrated efforts in the literature to understand the distributional properties of the sample distance covariance in a high-dimensional setting, with an exclusive emphasis on the null case that $X$ and $Y$ are independent. This paper derives the first non-null central limit theorem for the sample distance covariance, and the more general sample (Hilbert–Schmidt) kernel distance covariance in high dimensions, in the distributional class of $(X,Y)$ with a separable covariance structure. The new non-null central limit theorem yields an asymptotically exact first-order power formula for the widely used generalized kernel distance correlation test of independence between $X$ and $Y$. The power formula in particular unveils an interesting universality phenomenon: the power of the generalized kernel distance correlation test is completely determined by $n\cdot \operatorname{dCor}^{2}(X,Y)/\sqrt{2}$ in the high-dimensional limit, regardless of a wide range of choices of the kernels and bandwidth parameters. Furthermore, this separation rate is also shown to be optimal in a minimax sense. The key step in the proof of the non-null central limit theorem is a precise expansion of the mean and variance of the sample distance covariance in high dimensions, which shows, among other things, that the non-null Gaussian approximation of the sample distance covariance involves a rather subtle interplay between the dimension-to-sample ratio and the dependence between $X$ and $Y$.