The purpose of this experiment was to determine the effects of sequential sounds on cortical auditory evoked potentials and to investigate temporal masking. The study tested the hypotheses that forward masking reduces the amplitude of the/ba/-evoked response for short intervals between masker offset and signal onset (Δt) but not for Δt's, and that it prolongs the latency of the response even for long Δt's. In addition, it was expected that this latency shift recovers to baseline as an inverse function of Δt. Cortical auditory evoked potentials evoked by the consonant-vowel/ba/ were measured in 32 young normal-hearing adults. This signal was either presented alone or in the presence of a preceding speech-shaped noise masker. When the masker was present, the Δt's were 3, 10, 32, or 100 msec. The masker was presented at 70 dB SPL, and the signal at 70 dB pSPL. The dependent variables were the N1-P2 amplitude and the N1 latency. The presence of the masker increased the N1 latency of the/ba/-evoked response but this prolongation was not dependent upon Δt. Similarly, the presence of the masker reduced the N1-P2 amplitude of the/ba/-evoked response but this reduction was not dependent upon Δt. The pattern of results did not support the hypotheses. Rather, they suggested that, for cortical auditory evoked potentials evoked by configurations of sequential sounds, a leading sound can affect the response to a lagging sound in a manner that is distinct from conventional forward-masking effects, where recovery functions are the norm.

Temperature-free loss function for contrastive learning.

In this work we investigated the far-field characteristics of ionic wind induced by the DC corona discharge of a needle-ring and/or single-needle electrode configuration in ambient air. Wind velocity, net ion flux and their spatial distribution were measured under various conditions and ion kinetic behavior was analyzed with an electrodynamic model. The results show that the ionic wind in the needle-ring corona is due to the inertia of ions accelerated between electrode gap, while the ionic wind in the single-electrode corona is formed by ions accelerated outside the needle, propagating as far as about 100 cm in space. Wind velocity depends on the distance, moving direction, total corona current, air density and ion mobility as well as the voltage polarity. In an axial axis, the ionic wind speed decreases with distance as a function of inverse square root, while the ion flux decreases with distance as an inverse quadratic function for both coronas. The electrodynamic model can well describe the motion of the ions as well as the ionic wind formation, revealing results being highly consistent with the experiment.

Sample size re-estimation designs using a promising zone framework are widely used adaptive trial methodologies that guide study continuation or modification during interim analyses. Conventional implementations often base interim calculations solely on participants with available primary endpoints, overlooking predictive information from baseline and earlier visits. This underutilization can lead to inefficient interim decision-making. In this work, we adapt semi-parametric efficient estimators that leverage baseline and intermediate data for use within a promising zone sample size re-estimation design. By incorporating information from participants who have not yet reached their primary endpoint, these estimators enable more precise interim estimators while maintaining strict Type I error control through the inverse normal combination function. Using data from the ADAPT study in generalized myasthenia gravis, we illustrate how these methods integrate into a promising zone sample size re-estimation framework. Simulations based on longitudinal profiles of anti-acetylcholine receptor antibody-seronegative participants demonstrate improved operating characteristics compared with the conventional approach, including increased overall power, especially for moderate effect sizes, without inflating the one-sided Type I error. Our findings highlight the practical benefit of applying existing semi-parametric estimators within promising zone sample size re-estimation designs, enabling more efficient and timely interim decision-making in settings with partially observed longitudinal data.

This paper proposes a key vulnerable node identification method based on the trend of short-circuit capacity change, and establishes a complete set of node vulnerability evaluation index system by analyzing the change of node short-circuit capacity before and after distributed power supply access. At the same time, this paper improves the traditional port compensation method, fully considering the influence of parallel branches and the nonlinear characteristics of distributed power supply. Combined with complex network theory, this study introduces indicators such as the proportionality coefficient and the association Q-function to deeply analyze the topological destruction resistance of active distribution networks. The results show that the short-circuit capacity varies from 17.39% to 21.95% at distributed power access points and their neighboring areas, which constitute the key vulnerable nodes of the system. This paper also proposes a stochastic model node-equivalent voltage crossing probability calculation method to simplify the impact analysis of multi-point stochastic modeling of power distribution networks through node equivalence. The probabilistic security analysis method based on Latin hypercube-Monte Carlo sampling considers multiple uncertainties and establishes a time series probabilistic tidal current calculation model. The results show that the penetration rate of distributed power supply is the main factor affecting system safety. In addition, the complex affine analysis and operation optimization method proposed in this paper effectively solves the affine approximation problem of suboperations such as trigonometric and inverse trigonometric functions, and reduces the network loss and voltage deviation. This study provides important theoretical value and engineering application significance for the planning and design, operation control and fault handling of active distribution networks.

Finite extensibility strongly influences the nonlinear dynamics of dilute polymer solutions, yet its representation in stochastic dumbbell models typically relies on approximate forms of the inverse Langevin function. Here, we systematically examine how commonly used inverse Langevin function approximations affect both the model predictions and numerical behavior of stochastic dumbbell models. Using the Brownian Configuration Field formulation, we directly integrate the full stochastic equations for finitely extensible dumbbells and compare three spring-force representations: the classical Finitely Extensible Nonlinear Elastic (FENE) model and two Padé-based approximations due to Cohen and Rickaby–Scott. Model predictions are assessed in large-amplitude oscillatory shear, steady uniaxial extensional, and capillary thinning flows for different parameter values. The results show that differences emerge when chains remain at moderate extension, whereas weakly deformed chains and chains rapidly driven to near-full extension exhibit model-independent behavior. In these transitional regimes, the FENE model consistently predicts lower stretch and stress levels than the Padé-based approximations, with discrepancies increasing for highly extensible chains. Analysis of the governing equations further demonstrates that the choice of approximation controls the stiffness of the stochastic dynamics near full extension, directly impacting numerical stability in coupled flow simulations. These results indicate that the choice of inverse Langevin approximation can measurably affect both model predictions and numerical robustness in stochastic simulations of nonlinear viscoelastic flows.

Let K ( r ) and arctanh ⁡ r be the complete elliptic integral of the first kind and inverse hyperbolic tangent function, respectively. In 2004, Alzer and Qiu conjectured that r ↦ G ( r ) = ln ⁡ ( 2 / π ) + ln ⁡ K ( r ) ln ⁡ arctanh ⁡ r − ln ⁡ r is strictly increasing and convex from ( 0 , 1 ) onto ( 3 / 4 , 1 ) . In this paper, we prove the stronger results than Alzer–Qiu's conjecture, that is, the functions − ( 1 / G ( x ) ) ′ , ( ln ⁡ G ( x ) ) ′ and G p ( x ) for all p>0 are all absolutely monotonic on ( 0 , 1 ) . This leads to a series of new sharp bounds for K ( r ) , which greatly improve and extend existing results. The significance of our findings lies not only in solving the Alzer–Qiu's conjecture and further establishing several related absolutely monotonic functions, but more importantly, in providing a new and effective approach to deal with the absolute monotonicity of fractional functions.

Planetary and geological melts and magmas produced at depth encounter rocks at a variety of temperatures and redox conditions during their ascension towards the surface of planetary bodies. Reactions occur between the magma and surrounding rock material, but despite their potential importance for the regulation of magmatic differentiation, the rates of such interactions are rarely considered and poorly known. The aim of this work is to review the results of high-temperature experiments and kinetic models for the dissolution of the main rock-forming minerals in aluminosilicate melts, that may be applied to partial melting of common rock types, and reactions between the melts and the principal rocks composing the lithosphere. A kinetic equation allowing the first-order prediction of mineral dissolution rates in planetary and geological melts was generated. The diffusion-controlled dissolution rate r (mol cm-2 s-1) of common rock-forming silicate minerals in aluminosilicate melts at 1300 ± 20 °C and <1 GPa pressure can be described by an inverse function of the viscosity of boundary layer melt (i.e. that formed at the crystal-melt interface upon the dissolution) independent of silicate mineral composition according to: r = k η-n, where the correlation coefficient k = 2 ×10-7 (mol cm-2 sn-1 Pan), n = 0.5, and η (Pa s) is the viscosity of the boundary layer melt (for η ≤105 Pa s). This function relating dissolution rate and melt viscosity is consistent with a simple detachment mechanism involving network-forming Si-O atoms during silicate mineral dissolution. This equation can be applied to the dissolution of the principal rock-forming minerals during melt-rock interactions in the lithosphere such as lithosphere assimilation. It shows that low-viscosity mafic-ultramafic magmas can be significantly more contaminated by lithosphere rock material compared to the high viscosity felsic magmas. This correlation for the main rock-forming minerals may be directly applicable to planetary lithosphere assimilation by magmas, magma mixing as well as the modeling of mantle metasomatism or other types of melt-rock interactions. Future efforts should be concentrated on developing kinetic models and providing further experimental constraints on the kinetic factors that control mineral-melt reactions in the terrestrial and planetary mantles.

Discrete event simulation models simulate times to events rather than using the cumulative survival probabilities provided by parametric survival models. This requires inversion of the survival functions to produce analytical solutions to derive these event times from given survival estimates. While numerical methods can approximate event times for more complex survival models, this process may be computationally expensive, especially when repeated over large numbers of simulations. We aimed to derive an analytical solution to inverse functions for Royston/Parmar restricted cubic spline parametric survival models and test the execution speed when implemented in Microsoft Excel against numerical approximation methods (Goal Seek) and a hybrid approach using Brent's root-solving algorithm. Three case types were classified according to the positioning of the given cumulative survival estimate " " between cumulative survival probabilities corresponding to the boundary knots from the Royston/Parmar restricted cubic spline model to determine the positioning of the solution "t" between knot values. For Case 1 (t before first knot) and Case 3 (t after last knot), a linear equation for ln(t) is produced, and single solutions are derived for t as a function of . For Case 2 (between boundary knots), a cubic equation of the form a 3 + b 2 + c + d = 0 is derived, with a published cubic equation-solving algorithm used to obtain the correct solution for t. Royston/Parmar restricted cubic spline models were then fitted to published colon cancer data, and used to test the average execution speed of a user-defined function coded in Visual Basic for Applications (VBA)based on the analytical inversion solution compared to two Goal Seek approaches (default and increased precision) and a hybrid approach using Brent's method in Microsoft Excel over 100 replications of event time simulations, for a range of given survival estimates between 1% and 99% for all fitted models. The mean (standard deviation) execution speed for the spline inversion user-defined function across 100 replications was 0.612 (0.029) seconds compared with 10.567 (0.175) seconds for the default Goal Seek approach, 12.230 (0.265) seconds for the increased precision Goal Seek approach and 1.140 (0.114) seconds for the hybrid Brent method, corresponding to 94.2%, 95.0%, and 46.3% reductions in average execution time, respectively. Analytical solutions to inverse functions of Royston/Parmar restricted cubic spline models can be derived to allow precise estimation of event times from given survival estimates and substantially increase simulation speed for event time generation in Microsoft Excel for discrete event simulation versus approximations using numerical methods, as well as facilitate derivation of a quantile function. Further research should be considered to test event time derivation speed in other software (such as R), extend the solution to time-varying covariates and identify other potential use cases for the analytical inversion solution.

This article proposes a data-driven inverse flux map for induction motors (IM) using a deep neural network (DNN). The proposed method enables the direct mapping of stator and rotor currents from flux linkages, which is essential for implementing flux map-based IM model, derived from finite element analysis (FEA). Thanks to this flux map-based IM model, fast and accurate IM simulation combined with inverter circuit models and control algorithms is possible. In the proposed method, the DNN is employed as a universal function approximator to model the inverse of the nonlinear multivariable vector function. The training data is obtained from static FEA. To enhance learning performance and modeling accuracy, the proposed method applies a whitening transformation and incorporates a tangent activation function. The proposed inverse flux map is validated based on the characteristics of the inverse function. The overall flux map-based IM model, integrated with the proposed inverse map, is further validated against time-stepping FEA (TS-FEA) and experimental results using two commercial IMs under various operating conditions.

In this article, we study the complexity of evaluating Conjunctive Queries with negation ( \(\mathsf {CQ}^{\lnot }\) ). First, we present an algorithm with linear preprocessing time and constant delay enumeration for a class of CQs with negation called free-connex signed-acyclic queries. We show that no other queries admit such an algorithm subject to lower-bound conjectures. Second, we extend our algorithm to Conjunctive Queries with negation and aggregation over a general semiring, which we call Functional Aggregate Queries with negation ( \(\mathsf {FAQ}^{\lnot }\) ). Such an algorithm achieves constant delay enumeration for the same class of queries but with a slightly increased preprocessing time, which includes an inverse Ackermann function. We show that this surprising appearance of the Ackermann function is probably unavoidable for general semirings but can be removed when the semiring has a specific structure. Finally, we show an application of our results to computing the difference of CQs.

Cable safety evaluation is crucial for cable-supported bridges in service. Due to its cost-effectiveness and convenience, vibration-based methods are widely used in cable monitoring. The damage detection and fatigue assessment of the cable using vibration data are developed in this paper. Firstly, a combination method of the FFT and block recursive amplitude and phase estimation is proposed to quickly and accurately track time-varying frequency based on acceleration data. Secondly, the time-varying cable frequency is applied to detect damage and identify the time-varying cable force, respectively. For damage detection, a combined method of the moving average and empirical mode decomposition is used to remove the effect of traffic and temperature in time-varying frequency, then a K-means clustering method is used for quantitative identification of cable damage. For the identification of time-varying cable force, a fast and accurate cable force formula is fitted based on the cable inverse analysis characteristic function. Finally, a scheme of real-time monitoring and sensing of cable fatigue based on the detected damage and identified time-varying cable forces and Miner linear fatigue damage accumulation theory is proposed. This method considers both the real stress amplitude spectrum of the cable and the change in the mechanical properties of cables simultaneously.

The purpose of the article is to identify and analyze the dramaturgical mechanisms of absurdity as a critical tool for interpreting social, political, and cultural realities in XXI century film comedy. The object of the study is contemporary absurd film comedy as a cultural and artistic phenomenon. The subject is the dramaturgical mechanisms of absurdity and their sociocritical function in three selected films. The relevance of the research lies in the growing role of absurd comedy as a form of philosophical and critical reflection in the post-truth era, where traditional analytical tools often prove insufficient to address crises of meaning, ideological constructs, and communicative collapse.The methodology of the theoretical analysis com-bines dramaturgical and genre-typological approaches with philosophical frameworks of the absurd — primarily A. Camus’ concept of the confrontation between the human quest for meaning and the world’s indifference — and cultural critique drawing on Baudrillard, Hutcheon, Eagleton, and others. The study applies close reading of three key films: The Death of Stalin (2017, dir. Armando Iannucci), Swiss Army Man (2016, dir. Daniel Kwan & Daniel Scheinert), and Triangle of Sadness (2022, dir. Ruben Östlund).The results. The analysis demonstrates how violation of logic, grotesque exaggeration, paradox, and hierarchical inversion function as critical dramaturgical tools in each film. In The Death of Stalin, absurdity exposes the irrational chaos and fear-driven bureaucracy of totalitarianism. Swiss Army Man uses bodily grotesque and existential nonsense to explore profound loneliness and the human need for connection. Triangle of Sadness deconstructs fictitious class hierarchies and simulacral roles in late capitalism through social satire. Absurd film comedy thus emerges as a distinctive philosophical language: laughter exposes social contradictions, cognitive fractures, ideological illusions, and commu-nicative failures.The scientific novelty of the research lies in the systematic description of absurdity specifically as a dramaturgical tool with a pronounced social vector — an approach not previously applied to this selection of contemporary films in the Ukrainian scholarly tradition.The practical significance of the article consists in the potential application of these findings in the professional training of directors and screenwriters, as well as within specialized academic disciplines in film studies and cultural criticism.

Near-infrared spectroscopy (NIR) is an emerging powerful tool with widespread applications across various industries, including mineral exploration and geo-metallurgical characterization. This technique is particularly attractive from an operational standpoint due to its ability to perform rapid and non-destructive measurements. In the geometallurgical field, NIR is primarily employed for the identification of NIR-active minerals that collectively influence the production process. A predictive mathematical model used to estimate a numeric value, like hardness, from a NIR spectral curve, may be referred to as a "chemometric model", represented by a function. The accuracy of chemometric models, like all predictive models, is highly reliant upon the availability of enough calibration samples to mathematically establish a relationship between the target variable and spectral signatures. The objective of this study is to present a methodology to evaluate the amount of calibration samples required to produce a sufficiently accurate chemometric model. An inverse function developed to simulate different scenarios of spectral curves is used. This tool enables the generation of multiple chemometric functions by varying the amount of data used for calibration. By employing an inverse function, it is possible to analyze how the number of calibration samples influences the associated variability or error. This approach allows for the establishment of a quantitative relationship between the calibration dataset size and the predictive model's reliability by calculating the percentage error from iterations using the simulated values. This study aims to determine the minimum number of samples required for the calibration of the chemometric model to ensure a prediction error below 3% for a specific target variable, demonstrated using hardness prediction. It is crucial that the selected calibration samples are spatially representative and free from sampling biases. It is important to highlight that the total error in the block model (for subsequent use in mine planning) results from the propagation of multiple sources of uncertainty, including QAQC, chemometric model reliability, NIR sample representativity, and the interpolation methodology used in the block model. However, this analysis focuses exclusively on the variability associated with the reliability of the chemometric model. This methodology was tested in a simulated case study and in a porphyry copper deposit in northern Chile.

The article comments on the fact that the economic reforms implemented in Azerbaijan have necessitated large investments in various sectors of the economy. In this regard, it is crucial to consider the risk factor associated with investments in the oil and gas sector, to select an effective option for achieving the set goal, and to conduct a thorough study. The analysis of technical and economic indicators in the economic justification of investments in oil and gas production areas is based on the determination of efficiency criteria using the inverse function method, distribution indicators of random variables and calculations based on probability theory. In addition, risk simulation modelling for the development and implementation of investment projects aimed at increasing oil production in the Azneft Production Union was carried out using GLONASS. A diagram of the dynamics of NPV (Net Present Value), HR (Hurdle Rate) and IRR (Internal Rate of Return) changes was constructed. The proposed methodology can make a significant contribution to the calculation of investments in the oil production sector.

Let \(\mathcal{S}_{cos}^{\ast }\) be the subclass of starlike functions \(f\) associated with cosine function defined by \(\left( zf^{\prime}(z)/f(z)\right) \prec \cos (z)\). In this paper, we obtain the sharp coefficient bounds and Hankel determinants of second order for the inverse logarithmic function for this class. We also present the best possible bounds of second order Toeplitz determinant for the functions in the same class.

ABSTRACT Full waveform inversion (FWI) is a powerful technique for estimating high‐resolution subsurface velocity models by minimizing the discrepancy between modelled and observed seismic data. However, the oscillatory nature of seismic waveforms makes point‐wise discrepancy measures highly prone to cycle skipping, especially when the initial velocity model is inadequate. To address this challenge, various alternative misfit functions have been proposed in the literature, each with unique strengths and limitations. Dynamic time warping (DTW) is a popular technique in signal processing for aligning time series using dynamic programming. While a differentiable variant of DTW has been recently proposed, its use in FWI is hindered by high‐frequency artefacts in the adjoint source and the substantial computational cost of gradient evaluations. In this study, we propose a neural network‐based approach to learn the time shifts that align two time series in a supervised manner. The trained network is then utilized to compare traces from observed and modelled seismic data, offering a stable and computationally efficient alternative to DTW. Furthermore, the inherent differentiability of neural networks via backpropagation enables seamless integration into the FWI framework as a misfit function. We validate this approach on two synthetic datasets, namely the Marmousi model and the Chevron blind test dataset, demonstrating in both cases a similar convergence behaviour to that of Soft‐DWT whilst drastically reducing the computational time of the adjoint source calculation.

Discrete chaotic maps in the real number field have been widely investigated and applied to various applications. However, there has been limited focus on constructing discrete chaotic maps with complicated dynamics in the complex field. In light of this, this article proposes a 1-D complex-variable chaotic model (1-D-CCM), which can produce a multitude of 1-D complex-variable chaotic maps by combining unbounded analytic functions and locally bounded analytic functions. To illustrate the effectiveness of 1-D-CCM, we construct two 1-D complex-variable chaotic maps by combining inverse trigonometric functions and hyperbolic trigonometric functions. We provide theoretical proof of a new 1-D complex-variable chaotic map as one example to demonstrate that the generated chaotic maps satisfy the chaos definition in terms of Lyapunov exponent. Property analysis reveals distinct strange attractors and hyperchaotic behaviors for the two 1-D complex-variable chaotic maps. Performance evaluations show that the example maps of 1-D-CCM model can achieve a 0–1 test value of 1.0017, a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$C_{0}$</tex-math></inline-formula> complexity of 0.7253, a correlation dimension of 2.0242, and a sample entropy of 0.8288. Experimental results demonstrate superior performance indicators compared to other representative chaotic maps. We construct a hardware platform using a microcontroller to implement the attractors of the two new complex-variable chaotic maps. Finally, we design pseudorandom number generators to demonstrate the potential applications of the two 1-D complex-variable chaotic maps.

Rapid calculation method for the safety factors of three-dimensional homogeneous slopes

This study evaluates the structural integrity of ship superstructures and examines the vibration characteristics of applied materials under operational loading conditions using finite element–based analyses. The structural safety of a composite ship superstructure was first investigated by considering wind loads in combination with six-degree-of-freedom (6-DOF) ship motions. All inverse response function (IRF) values remained below unity, confirming that the structural safety of the superstructure is maintained under combined wind loading and 6-DOF motion conditions. In addition, this study examined the feasibility of replacing conventional metallic superstructures with lightweight composite materials to achieve hull weight reduction and to assess fatigue durability against vibration-induced damage through computational simulation prior to practical application. The results indicate that a hybrid laminate configuration combining carbon fiber and glass fiber is effective in ensuring structural safety. The laminate architecture efficiently distributes applied loads, thereby reducing stresses acting on individual plies as well as on the overall structure. Furthermore, the composite superstructure was shown to withstand wind loading, six-DOF motions and vibratory environments without degradation of structural integrity.