Empirical Parameters Research Articles

Science Outcome Design Parameters for Cluster-Randomized Trials Involving Teachers

Programs aiming to improve student science outcomes often involve teachers. When designing cluster-randomized trials (CRTs) to evaluate the causal effects of these programs, investigators need empirical design parameters as critical inputs in the study design phase. Using proper empirical design parameters to conduct power analysis, investigators can ensure designs have adequate statistical power to detect treatment effects and efficiently use resources. The current study uses two nationally representative samples to estimate empirical design parameters for science outcomes in settings of students (nested within teachers) nested within schools. We compile design parameters for intraclass correlation coefficients and proportions of variance explained by covariates. We illustrate how to use the results to design efficient and effective CRTs in both the conventional statistical power analysis framework and the optimal design framework that additionally considers sampling costs.

Effect of Silver Nanoparticle Size on Antibacterial Activity

The ubiquitous use of products containing AgNPs results in the entry of nanoparticles into the environment. Both nanoparticles and Ag+ released upon their oxidative dissolution have a toxic effect on living microorganisms. The antibacterial activity of spherical silver nanoparticles of 10.8 ± 0.8 nm and 22.7 ± 2.2 nm in size stabilized by carbonate ions was studied against Escherichia coli and other bacteria. The biocidal action of silver increases as the particle size decreases. Analysis of these results and other known data made it possible to substantiate a linear proportional relationship between the minimum inhibitory concentration (MIC) or the half-maximal inhibitory concentration (IC50) and silver nanoparticle size and determine empirical parameters for this relationship. The antibacterial activity (toxicity) is directly proportional to the specific surface area of nanosized silver.

Computational Analysis of S1PR1 SNPs Reveals Drug Binding Modes Relevant to Multiple Sclerosis Treatment

Background/Objectives: Multiple sclerosis (MS) is an autoimmune disorder of the central nervous system (CNS) characterized by myelin and axonal damage with a globally rising incidence. While there is no known cure for MS, various disease-modifying treatments (DMTs) exist, including those targeting Sphingosine-1-Phosphate Receptors (S1PRs), which play important roles in immune response, CNS function, and cardiovascular regulation. This study focuses on understanding how nonsynonymous single nucleotide polymorphisms (rs1299231517, rs1323297044, rs1223284736, rs1202284551, rs1209378712, rs201200746, and rs1461490142) in the S1PR1’s active site affect the binding of endogenous ligands, as well as different drugs used in MS management. Methods: Extensive molecular dynamics simulations and linear interaction energy (LIE) calculations were employed to predict binding affinities and potentially guide future personalized medicinal therapies. The empirical parameters of the LIE method were optimized using the binding free energies calculated from experimentally determined IC50 values. These optimized parameters were then applied to calculate the binding free energies of S1P to mutated S1PR1, which correlated well with experimental values, confirming their validity for assessing the impact of SNPs on S1PR1 binding affinities. Results: The binding free energies varied from the least favorable −8.2 kcal/mol for the wild type with ozanimod to the most favorable −16.7 kcal/mol for the combination of siponimod with the receptor carrying the F2055.42L mutation. Conclusions: We successfully demonstrated the differences in the binding modes, interactions, and affinities of investigated MS drugs in connection with SNPs in the S1PR1 binding site, resulting in several viable options for personalized therapies depending on the present mutations.

Optical and Radio Analysis of Systematically Classified Broad-lined Type Ic Supernovae from the Zwicky Transient Facility

We study a magnitude-limited sample of 36 broad-lined type Ic supernovae (SNe Ic-BL) from the Zwicky Transient Facility Bright Transient Survey (detected between 2018 March and 2021 August), which is the largest systematic study of SNe Ic-BL done in literature thus far. We present the light curves (LCs) for each of the SNe and analyze the shape of the LCs to derive empirical parameters, along with the explosion epochs for every event. The sample has an average absolute peak magnitude in the r band of M¯r,max=−18.51±0.15 mag. Using spectra obtained around peak light, we compute expansion velocities from the Fe ii 5169 Å line for each event with high enough signal-to-noise ratio spectra, and find an average value of vph¯=16,100±1100 km s−1. We also compute bolometric LCs, study the blackbody temperature and radii evolution over time, and derive the explosion properties of the SNe. The explosion properties of the sample have average values of M¯Ni=0.37−0.06+0.08M⊙ , M¯ej=2.45−0.41+0.47M⊙ , and E¯K=(4.02−1.00+1.37)×1051 erg. Thirteen events have radio observations from the Very Large Array, with eight detections and five non-detections. We find that the populations that have radio detections and radio non-detections are indistinct from one another with respect to their optically inferred explosion properties, and there are no statistically significant correlations present between the events’ radio luminosities and optically inferred explosion properties. This provides evidence that the explosion properties derived from optical data alone cannot give inferences about the radio properties of SNe Ic-BL and likely their relativistic jet formation mechanisms.

Rolling bearing fault diagnosis based on acoustic-vibration data fusion and mode decomposition combined with the crested porcupine optimization algorithm

Variational Mode Decomposition (VMD) is extensively utilized in the domain of rotating machinery fault diagnosis. Nevertheless, the reliance on empirical parameter tuning and the limitations inherent in traditional single-signal (either vibration signals or acoustic signals) fault diagnosis methods present substantial challenges. These include incomplete information and high sensitivity to noise. To address these shortcomings, a new method is introduced that integrates multi-modal sensor data and implements an adaptive VMD approach, enhanced through the Crested Porcupine Optimization Algorithm (CPO) to automatically optimize the key parameter. Then, uses optimized VMD to decompose the time series into intrinsic mode functions of different frequencies to capture the multi-scale characteristics of data. Finally, the decomposed acoustic-vibro signal components are fed into the CNN-BiGRU-AT network, which learns the spatio-temporal dependencies to enhance the accuracy of fault classification. The experimental results conducted across diverse high-noise environments demonstrate that this method’s superior noise robustness compared to single-modality sensor approaches， highlighting the method's potential for machinery fault detection in noisy conditions.

Memory Effects Explain the Fractional Viscosity Dependence of Rates Associated with Internal Friction: Simple Models and Applications to Butane Dihedral Rotation.

Barrier-crossing rates of biophysical processes, ranging from simple conformational changes to protein folding, often deviate from the Kramers prediction of an inverse viscosity dependence. In many recent studies, this has been attributed to the presence of internal friction within the system. Previously, we showed that memory-dependent friction arising from the nonequilibrium solvation of a single particle crossing a smooth one-dimensional barrier can also cause such a deviation and be misinterpreted as internal friction. Here we introduce a simple diatom model and show that even in the absence of explicit solvent, internal memory effects arise due to coupling of the reaction coordinate motion with frictionally orthogonal degrees of freedom. This results in a fractional viscosity dependence and a deviation from Kramers' theory, typically attributed to the presence of internal friction. This model therefore mimics several biological processes where a local conformational change of a biomolecule is often influenced by its surroundings. This gives rise to an apparent "internal friction" commonly measured in terms of empirical fitting parameters α and σ. We propose a microscopic measure of this internal friction using Grote-Hynes theory which employs memory-dependent friction. We use butane to demonstrate the effect of coupling strength on the internal friction in realistic systems. This model therefore can serve the purpose of understanding internal friction in biological systems in terms of such coupling.

Rhombohedral phase high-entropy alloy of AlMnCuZnBi as a photo-Fenton catalyst for methyl orange degradation

The formation of solid solutions with five or more elements having nearly equiatomic contributions termed as high entropy alloys (HEA), is recent strategy for the development of new materials. Such alloys have displayed superior properties than the conventional ones. The prepared alloys are generally face- or body-centered cubic structures with a few exceptions for orthorhombic and hexagonal close packed structure. In this, we report the synthesis of HEA of AlMnCuZnBi having rhombohedral crystal structure. The material was prepared by vacuum arc melting route. Both the diffractions (X-ray and electron) confirm its structure. The calculated thermodynamic empirical parameters e.g. ΔSmix, ΔHmix, δ, VEC and Ω even validate the feasibility of this single phase solid solution. The HEA had shown feeble ferromagnetic behaviour. The rhombohedral structured HEA may open up new possibilities for various emerging applications. The proposed HEA acted as a catalyst for photo-Fenton like reaction and could degraded methyl orange dye completely in 170 minutes.

Quantitative Multi-Parametric MRI of the Prostate Reveals Racial Differences

Purpose: This study investigates whether quantitative MRI and histology of the prostate reveal differences between races, specifically African Americans (AAs) and Caucasian Americans (CAs), that can affect diagnosis. Materials and Methods: Patients (98 CAs, 47 AAs) with known or suspected prostate cancer (PCa) underwent 3T MRI (T2W, DWI, and DCE-MRI) prior to biopsy or prostatectomy. Quantitative mpMRI metrics: ADC, T2, and DCE empirical mathematical model parameters were calculated. Results: AAs had a greater percentage of higher Gleason-grade lesions compared to CAs. There were no significant differences in the quantitative ADC and T2 values between AAs and CAs. The cancer signal enhancement rate (α) on DCE-MRI was significantly higher for AAs compared to CAs (AAs: 13.3 ± 9.3 vs. CAs: 6.1 ± 4.7 s−1, p < 0.001). The DCE signal washout rate (β) was significantly lower in benign tissue of AAs (AAs: 0.01 ± 0.09 s−1 vs. CAs: 0.07 ± 0.07 s−1, p < 0.001) and significantly elevated in cancer tissue in AAs (AAs: 0.12 ± 0.07 s−1 vs. CAs: 0.07 ± 0.08 s−1, p = 0.02). DCE significantly improves the differentiation of PCa from benign in AAs (α: 52%, β: 62% more effective in AAs compared to CAs). Histologic analysis showed cancers have a greater proportion (p = 0.04) of epithelium (50.9 ± 12.3 vs. 44.7 ± 12.8%) and lower lumen (10.5 ± 6.9 vs. 16.2 ± 6.8%) in CAs compared to AAs. Conclusions: This study shows that AAs have different quantitative DCE-MRI values for benign prostate and prostate cancer and different histologic makeup in PCa compared to CAs. Quantitative DCE-MRI can significantly improve the performance of MRI for PCa diagnosis in African Americans but is much less effective for Caucasian Americans.

Empirical interatomic potential development and classical molecular dynamics simulation of monolayer group-III monochalcogenides: insights into thermal transport properties

Abstract This research addresses the lack of comprehensive studies utilizing classical molecular dynamics simulations for monolayer group-III monochalcogenide materials. These materials, including GaS, GaSe, and InSe, have shown promise for diverse applications but lack well-defined empirical interatomic potentials in the literature. This study is concentrated on the development of empirical interatomic potential parameters for these materials using the particle swarm optimization method, filling a gap in the literature regarding classical molecular dynamics simulations. The parameters are optimized based on fundamental physical characteristics such as the lattice constants, bond lengths, phonon dispersions, and the equation of state, obtained from first-principles calculations. The developed potential parameters are then employed to predict lattice thermal conductivity through non-equilibrium classical molecular dynamics simulations, providing insights into the thermal transport properties of these materials.

Multifactorial Analysis of the Effect of Applied Gamma-Polyglutamic Acid on Soil Infiltration Characteristics

To investigate the mechanism and influence of applying gamma-polyglutamic acid (γ-PGA) on soil water infiltration, laboratory experiments and numerical simulations were conducted using Hydrus-1D. These studies assessed the impact of various application rates of γ-PGA on soil water characteristic parameters. Orthogonal simulation experiments on soil bulk density, γ-PGA application rates, and burial depths were performed utilizing predefined soil water characteristic values (twelve groups: nine groups of numerical simulation experiments and three groups of laboratory verification tests), and the soil infiltration characteristics were analyzed. Concurrently, an empirical model was developed to elucidate the relationships between the empirical model parameters and influencing factors, as well as to examine the sensitivity of these factors to changes in soil infiltration rate. The relationship between cumulative infiltration and the distance of wetting front movement, based on the water balance equation, was refined. The results indicated that γ-PGA significantly affected soil water characteristic parameters, where the saturated water content and the reciprocal of soil intake suction increased with rising γ-PGA applications (p < 0.01), while the saturated hydraulic conductivity and the parameter n decreased (p < 0.01), with no notable changes in the retained water content (p > 0.05). The trend in cumulative infiltration influenced by various factors could be modeled by a capacitive charging model function, which yielded a superior fit. A negative correlation existed between the sensitivity index and all the influencing factors (p < 0.05), with the order of influence being soil bulk density, γ-PGA application rate, and γ-PGA burial depth, respectively. Utilizing the modified water balance equation, the ratio of cumulative infiltration to wetting front migration distance corresponded more closely with a power function. These findings provide a theoretical foundation for further studies on the effects of γ-PGA on crop growth characteristics in fields and the optimization of γ-PGA technical element combinations.

Estimating ground motion intensities using simulation-based estimates of local crustal seismic response

Abstract. It is estimated that 2 billion people will move to cities in the next 30 years, many of which possess high seismic risk, underscoring the importance of reliable hazard assessments. Current ground motion models for these assessments typically rely on an extensive catalogue of events to derive empirical ground motion prediction equations (GMPEs), which are often unavailable in developing countries. Considering the challenge, we choose an alternative method utilizing physics-based (PB) ground motion simulations and develop a simplified decomposition of ground motion estimation by considering regional attenuation (Δ) and local site amplification (A), thereby exploring how much of the observed variability can be explained solely by wave propagation effects. We deterministically evaluate these parameters in a virtual city named Tomorrowville, located in a 3D-layered crustal velocity model containing sedimentary basins, using randomly oriented extended sources. Using these physics-based empirical parameters (Δ and A), we evaluate the intensities, particularly peak ground acceleration (PGA), of hypothetical future earthquakes. The results suggest that the estimation of PGA using the deterministic Δ−A decomposition exhibits a robust spatial correlation with the PGA obtained from simulations within Tomorrowville. This method exposes an order-of-magnitude spatial variability in PGA within Tomorrowville, primarily associated with the near-surface geology and largely independent of the seismic source. In conclusion, advances in PB simulations and improved crustal structure determination offer the potential to overcome the limitations of earthquake data availability to some extent, enabling prompt evaluation of ground motion intensities.

Revisiting the effect of lens mass models in cosmological applications of strong gravitational lensing

Abstract Strong gravitational lens system catalogues are typically used to constrain a combination of cosmological and empirical power-law lens mass model parameters, often introducing additional empirical parameters and constraints from high resolution imagery. We investigate these lens models using Bayesian methods through a novel alternative that treats spatial curvature via the non-FLRW timescape cosmology. We apply Markov Chain Monte Carlo methods using the catalogue of 161 lens systems of Chen et al. (2019) in order to constrain both lens and cosmological parameters for: (i) the standard ΛCDM model with zero spatial curvature; and (ii) the timescape model. We then generate large mock data sets to further investigate the choice of cosmology on fitting simple power-law lens models. In agreement with previous results, we find that in combination with single isothermal sphere parameters, models with zero FLRW spatial curvature fit better as the free parameter approaches an unphysical empty universe, ΩM0 → 0. By contrast, the timescape cosmology is found to prefer parameter values in which its cosmological parameter, the present void fraction, is driven to fv0 → 0.73 and closely matches values that best fit independent cosmological data sets: supernovae Ia distances and the cosmic microwave background. This conclusion holds for a large range of seed values fv0 ∈ {0.1, 0.9}, and for timescape fits to both timescape and FLRW mocks. Regardless of cosmology, unphysical estimates of the distance ratios given from power-law lens models result in poor goodness of fit. With larger datasets soon available, separation of cosmology and lens models must be addressed.

Prediction of the optimal hydrogen storage in high entropy alloys

Hydrogen is the most abundant element in nature, characterized by its vast resources, recyclability, and environmentally friendly. Also, it can exist in various forms, such as gas, liquid, or solid, to meet different storage needs. In solid-state storage, the hydrogen storage alloys have received widespread attention due to hydrogen is stored in the form of hydrides. In recent years, high entropy alloys (HEAs), as a new type of novel alloy design concept have attracted a lot of attention in many fields including hydrogen storage due to their unique structures and excellent properties. Moreover, the freedom of element selection leads to various types of HEAs, further enhancing the potential for their application in hydrogen storage. This article focuses on the hydrogen storage performance of HEAs and provides a comprehensive overview of the hydrogen storage mechanism, thermodynamics, and kinetics. Additionally, we summarize and compare the hydrogen storage capacities of previously published HEAs and introduce two empirical parameters, valence electron concentration (VEC) and atomic size difference (δ), and their relationship with hydrogen storage capacity. By applying the K-means clustering algorithm, we conclude that the optimal hydrogen storage capacity of HEAs occurs when 4 <VEC < 6 and 5.3 % <δ < 7.5 %. This finding offers valuable guidance for the future design of efficient hydrogen storage HEAs.

FedADMM-InSa: An inexact and self-adaptive ADMM for federated learning

Federated learning (FL) is a promising framework for learning from distributed data while maintaining privacy. The development of efficient FL algorithms encounters various challenges, including heterogeneous data and systems, limited communication capacities, and constrained local computational resources. Recently developed FedADMM methods show great resilience to both data and system heterogeneity. However, they still suffer from performance deterioration if the hyperparameters are not carefully tuned. To address this issue, we propose an inexact and self-adaptive FedADMM algorithm, termed FedADMM-InSa. First, we design an inexactness criterion for the clients’ local updates to eliminate the need for empirically setting the local training accuracy. This inexactness criterion can be assessed by each client independently based on its unique condition, thereby reducing the local computational cost and mitigating the undesirable straggle effect. The convergence of the resulting inexact ADMM is proved under the assumption of strongly convex loss functions. Additionally, we present a self-adaptive scheme that dynamically adjusts each client’s penalty parameter, enhancing algorithm robustness by mitigating the need for empirical penalty parameter choices for each client. Extensive numerical experiments on both synthetic and real-world datasets have been conducted. As validated by some tests, our FedADMM-InSa algorithm improves model accuracy by 7.8% while reducing clients’ local workloads by 55.7% compared to benchmark algorithms.

A Robust Static Model of Basic Oxygen Furnace for Analyzing Emerging Steelmaking Scenarios

A robust static model, which incorporates emerging steelmaking scenarios in terms of solid charge mix with the given hot metal in basic oxygen furnace process, is developed. It employs mass and enthalpy balances to comprehend nonequilibrium conditions, considering four key empirical parameters: iron loss, post‐combustion ratio, heat loss, and undissolved lime content in slag, which are fine‐tuned using plant data through a multivariate approach, ensuring the reliability. The model is validated in a basic oxygen furnace (BOF) shop using data from over 4000 heats, achieving a strike rate of ≈77% for input lime prediction within ±1 ton and ≈80% for input oxygen prediction within ±600 Nm3. Model implementation in BOF shop provides valuable guidance to the operators, resulting in the reduction of average oxygen and lime consumption by 139 Nm3 and 652 kg heat−1, respectively. The model also enables the determination of the maximum scrap utilization of ≈16% for 0.8% silicon and ≈14% for 0.6% silicon in hot metal, respectively. The model aids in calculating the maximum tap temperature for varying hot metal silicon and iron ore addition. Overall, the model optimizes primary steelmaking, enhancing efficiency, reducing resource consumption, and offering insights into alternative iron sources like direct reduced iron.

PRIME: A CyberGIS Platform for Resilience Inference Measurement and Enhancement

In an era of increased climatic disasters, there is an urgent need to develop reliable frameworks and tools for evaluating and improving community resilience to climatic hazards at multiple geographical and temporal scales. Defining and quantifying resilience in the social domain is relatively subjective due to the intricate interplay of socioeconomic factors with disaster resilience. To broaden upon it, the choice of indicators and their subsequent ranking for the aggregation into an index is subjective in nature. This aggregation is not empirically validated and is prone to omit the nuances of localized resilience changes and causal factors affecting it, while leading to oversimplified conclusions. Meanwhile, there is a lack of scientifically and computationally rigorous, user-friendly tools that can support customized resilience assessment with consideration of local conditions. This study addresses these gaps through the power of CyberGIS with three objectives: 1) To develop an empirically validated disaster resilience model - Customizable Resilience Inference Measurement (RIM), designed for multi-scale community resilience assessment and influential socioeconomic factors identification; 2) To implement a Platform for Resilience Inference Measurement and Enhancement (PRIME) module in the CyberGISX platform backed by high-performance computing, enabling users to apply and customize RIM to compute and visualize disaster resilience; 3) To demonstrate the utility of PRIME through a representative study to understand the geographical disparities of county-level community resilience to natural hazards in the United States and identifying the driving factors of resilience in the social domain. Customizable RIM generates vulnerability, adaptability, and overall resilience scores derived from empirical parameters—hazard threat, damage, and recovery. Computationally intensive Machine Learning (ML) methods are employed to explain the intricate relationships between these scores and socioeconomic driving factors. PRIME provides a web-based notebook interface guiding users to select study areas, configure parameters, calculate and geo-visualize resilience scores, and interpret socioeconomic factors shaping resilience capacities. A representative study showcases the efficiency of the platform while explaining how the visual results obtained may be interpreted. The essence of this work lies in its comprehensive architecture that encapsulates the requisite data, analytical and geo-visualization functions, and ML models for resilience assessment. This setup provides a foundation for assessing resilience and strategizing enhancement interventions.

Nonparametric and Continuous Variable-Based Stratigraphic Modelling from Sparse Boreholes using Signed Distance Function and Bayesian Compressive Sensing

An accurate stochastic interpretation of subsurface stratigraphy with quantified uncertainty can benefit the subsequent risk management of geotechnical infrastructure. Traditional approaches to developing geological cross-sections from sparse boreholes typically require the calibration or definition of empirical model parameters and functions, which may introduce subjectivity and bias. In this study, a non-parametric and continuous variable-based spatial predictor that leverages the signed distance function and Bayesian compressive sensing (BCS) is proposed for subsurface stratigraphic modelling. The proposed method transforms sparse categorical borehole data from a low-dimensional space into continuous variables in a high-dimensional space, enabling a comprehensive representation of more implicit characteristics of intricate geological patterns. This transformation facilitates the use of the continuous-variable-based BCS for non-parametric spatial prediction. The most probable geological cross-section and uncertainty qualification plot are derived after transforming spatially interpreted fields of continuous variables back into soil types. The performance of the proposed method is demonstrated using synthetic and real-world cases. Results indicate that the proposed approach can handle intricate stratigraphic scenarios characterized by complex geological structures, such as crossed-inclined, folded, inclined-folded, and interbedded strata, in a data-driven and non-parametric manner. The advantages of the proposed method over existing spatial predictors for developing geological cross-sections are also demonstrated.

An Improved Model for Prediction of Critical Velocity of Cold-Spray by First-Principles Calculations

The first-principles calculation was applied to predict the critical velocity of Cu/Al cold-spray bonding for the first time. The bonding mechanism of cold-spray was clarified by analyzing the energy variation and atomic interaction during the cold-spray impact process. Our results showed that the shear deformation played a key role in the cold-spray bonding. The atomic interaction determined the effective absorption of impact kinetic energy and finally determined the successful bonding of the cold-spray. The heterogeneous atoms absorbed the impact kinetic energy by interatomic attraction to achieve cold-spray bonding, while the homogeneous atoms absorbed the impact kinetic energy by the deformation of interface layers. An excellent agreement between the predicted critical velocity and the experimental one could be obtained, especially for the heterogeneous material cold-spray. Our present method proved to be a simple and highly efficient computing method in critical velocity prediction. Most importantly, the critical velocity for cold-spray could be predicted without using any empirical or experimental parameters.

Geometric Scaling Law in Real Neuronal Networks.

We investigate the synapse-resolution connectomes of fruit flies across different developmental stages, revealing a consistent scaling law in neuronal connection probability relative to spatial distance. This power-law behavior significantly differs from the exponential distance rule previously observed in coarse-grained brain networks. We demonstrate that the geometric scaling law carries functional significance, aligning with the maximum entropy of information communication and the functional criticality balancing integration and segregation. Perturbing either the empirical probability model's parameters or its type results in the loss of these advantageous properties. Furthermore, we derive an explicit quantitative predictor for neuronal connectivity, incorporating only interneuronal distance and neurons' in and out degrees. Our findings establish a direct link between brain geometry and topology, shedding lights on the understanding of how the brain operates optimally within its confined space.

Trigger mechanism for a singing cavitating tip vortex

The discrete tone radiated from tip vortex cavitation (TVC), known as ‘vortex singing’, was recognized in 1989, but its triggering remains unclear for over thirty years. In this study, the desinent cavitation number and viscous correction are applied to describe the dynamics of cavitation bubbles and the dispersion relation of cavity interfacial waves. The wavenumber-frequency spectrum of the cavity radius from the experiment in CSSRC indicates that singing waves predominantly consist of the stationary double helical modes (kθ = 2- and -2+) and the breathing mode (kθ = 0-), rather than standing waves as assumed in previous literatures. Moreover, two trigger mechanisms, expressed by two triggering lines, are proposed: the twisted TVC, initially at rest, is driven into motion through the corrected natural frequency (fn) due to the step change of the far-field pressure. Subsequently, the frequency associated with the zero-group-velocity point (ῶzgv) at kθ = 0- is excited through ῶi, the frequency at the intersection of dispersion curves at kθ = 0- and -2+, or ῶj, the frequency at the intersection of dispersion curves at kθ = 0- and 2-, corresponding to two types of the vortex singing triggering. These solutions, without empirical parameters, are validated using singing conditions provided by CSSRC and G.T.H., respectively. Furthermore, the coherence and the cross-power spectral density spectrum indicates a large-scale breathing wave propagating along the singing cavity surface and travelling from downstream to hydrofoil tip, providing us a comprehensive understanding for the triggering of vortex singing.