Power Function Research Articles

Fosfomycin trometamol may be a valuable option for antimicrobial prophylaxis before urological surgery for benign prostatic hyperplasia. The objective is to develop a population pharmacokinetic model of a novel oral fosfomycin prophylactic scheme in the plasma and prostate of patients undergoing endoscopic surgery for benign prostatic hyperplasia. One- and two-compartment plasma pharmacokinetic models were fitted to fosfomycin plasma data, and different plasma-prostate linked models were tested by means of non-linear mixed effects modelling. Monte Carlo simulation was used to obtain 1000-subject concentration-time profiles of fosfomycin in the prostate. Probabilities of target attainment ≥ 90% of an area under the plasma concentration-time curve/minimum inhibitory concentration (MIC) > 83.3 and of a 70%t > MIC in the prostate were considered as optimal. Cumulative fractions of response against both wild-type and extended-spectrum beta-lactamase-producing Escherichia coli were calculated. A total of 104 patients, each providing a pair of plasma and prostate concomitant samples were included in the study. A one-compartment pharmacokinetic model was used to describe plasma fosfomycin concentration. Fosfomycin plasma-prostate relationships were adequately described by a direct response model with a power function. Simulations showed that fosfomycin disposition in the prostate was closely related to that in plasma. Optimal probabilities of target attainments were ensured against Enterobacterales having an MIC up to 0.5-1 mg/L in the 12 h vulnerable period after completing the prophylactic scheme. A prophylactic regimen of two doses of oral fosfomycin trometamol 3 g 12 h apart before undergoing prostatic surgery may grant effective concentrations in the prostatic tissue of patients for a 12 h vulnerable period.

There was positive power function correlation between tensile strength and root diameter, and a negative power function correlation between tensile strength and root diameter after single, mild and severe cyclic loading. Cyclic load significantly increased the root tensile force and strength. Compared with single load, the tensile force increased by 22.61 and 47.61%, and the tensile strength increased by 20.38 and 43.85% after mild and severe cyclic load, respectively. The strength of the root-soil complex of Artemisia nigra were linearly positively correlated with the vertical load. The greater the depth of the burying root, the lower the soiling efficiency. The strength and cohesion of the root-soil composite under the condition of soil pore water pressure is less than that of the soil pore water. The internal friction angle are positive growth rates under different soil pore water pressure conditions. The strength characteristics of the root-soil composite increase with increasing root diameter. The shear rate has no significant effect on the strength characteristics of the root-soil composite. Bangladesh J. Bot. 54(3): 667-676, 2025 (September) Special

Deep neural network (DNN) deployment has been confined to larger hardware devices due to their expensive computational requirements. This challenge has recently reached another scale with the emergence of large language models (LLMs). In order to reduce both their memory footprint and latency, a promising technique is quantization. It consists in converting floating point representations to low bit-width fixed point representations, usually by assuming a uniform mapping onto a regular grid. This process, referred to in the literature as uniform quantization, may however be ill-suited as most DNN weights and activations follow a bell-shaped distribution. This is even worse on LLMs whose weight distributions are known to exhibit large, high impact, outlier values. In this work, we propose an improvement over the most commonly adopted way to tackle this limitation in deep learning models quantization, namely, non-uniform quantization. NUPES leverages automorphisms to preserve the scalar multiplications. Such transformations are derived from power functions. However, the optimization of the exponent parameter and weight values remains a challenging and novel problem which could not be solved with previous post training optimization techniques which only learn to round up or down weight values in order to preserve the predictive function. We circumvent this limitation with a new paradigm: learning new quantized weights over the entire quantized space. Similarly, we enable the optimization of the power exponent, i.e. the optimization of the quantization operator itself during training by alleviating all the numerical instabilities. The resulting predictive function is compatible with integer-only low-bit inference. We show the ability of the method to achieve state-of-the-art compression rates in both, data-free and data-driven configurations. Our empirical benchmarks highlight the ability of NUPES to circumvent the limitations of previous post-training quantization techniques on transformers and large language models in particular.

Abstract In the process of filling body service, the two-step mining is affected by large-scale blasting activities, resulting in the gradual accumulation and expansion of micro-damage within the filling body until macro-crack formation, eventually triggering the structural instability and even collapse of the filling body. Thus, studying the dynamic response characteristics of filling body under explosion disturbance is critical. In this paper, the damage evolution and influence mechanism of filling body under explosion disturbance were investigated based on the ore-filling body explosion loading model and fractal theory. The results show that the failure mode of the filling body is manifested as random crack propagation and morphology. When the blasting disturbance intensity is low, the primary failure mode is a single radial crack. However, the failure mode changes to a ring-radial composite crack mode when the blasting disturbance intensity is high. There was an approximate power function relationship between the damage degree of the filling body and von Mises peak strain, whereas a linear relationship between the interface distance of the blast source and the amount of explosive and the damage degree of the filling body was found, in which the interface distance of the blast source had a more pronounced effect on the damage degree of the filling body. It was also found that optimizing the distance of the interface of the blast source is a more critical factor in controlling damage to the filling body.

The application of rubber in geotechnical engineering has gained widespread popularity due to its potential to enhance the engineering properties of foundation fills while reducing environmental pollution. This study focuses on investigating the influence of the rubber fiber content on the performance of calcareous sand by conducting a series of triaxial tests. The effects of the rubber fiber content and axial pressure on the strength, deformation, permeability, and particle breakage of rubber–calcareous sand were systematically studied. The experimental results reveal that increasing the rubber fiber content reduces the strength of rubber–calcareous sand, but it also inhibits the shear dilation and mitigates the occurrence of rupture surfaces: the sample with a rubber content of more than 10% only has shear-contraction. Both the rubber fiber content and axial stress contribute to the increased impermeability of rubber-modified calcareous sand, although they exhibit different characteristics. The relationship between the rubber fiber content and permeability coefficient is linear, while, under increasing axial stress, the permeability coefficient initially decreases rapidly; when the deviatoric stresses exceeds 1000 kPa, the decreasing rate slows down. Furthermore, rubber fiber significantly reduces particle breakage in calcareous sand. The relationship between the input energy applied to rubber-modified calcareous sand and the relative breakage rate of calcareous sand can be well-fitted with a power function. Samples with a higher rubber fiber content exhibit a lower relative breakage rate of calcareous sand under the same absorbed input energy. Through the research results of this paper, the best rubber ratio can be selected as the road filler in engineering practice to ensure both cost-effectiveness and environmental protection.

In this research, a comprehensive cross-route collision risk assessment model was developed with the aim of accurately determining the minimum safety interval for aircraft during cross-route flights. At the beginning of the study, the event tree analysis (ETA) method was adopted to meticulously break down the aircraft’s flight process. Subsequently, a stochastic differential equation was established based on the route structure to precisely describe the aircraft’s position change. The Monte Carlo method was then utilised to calculate the probability of conflicts. When the air traffic control officer’s (ATCO) deployment malfunctions and is likely to trigger an alarm, the fault tree (FT) and dynamic event tree (DET) analysis methods were further employed. These two methods were used to calculate the failure probability of the warning system and the pilot’s operation error probability respectively, thereby obtaining the failure probability during the warning adjustment process. The completed comprehensive assessment model has powerful functions and can efficiently simulate and accurately evaluate collision risks under different initial conditions.

This study employs Conceptual Integration Theory as its theoretical framework, supplemented by optimization principles and model types. It focuses on the characteristic nation-family construction elements within the lyrics of “Great China”, conducting an integrated analysis of its conceptual bundles to reveal the philosophical conception of “nation-family unity”within mainstream musical works. Findings indicate that “Great China” intertwines “family” and “nation” through themes of ethnicity, destiny, growth, and emotion, demonstrating the powerful ideological shaping function of mainstream works in the contemporary era. The family-nation perspective permeating such works not only reflects ancient wisdom but also lays the foundation for the unity and collective resolve of the Chinese nation today, further propelling the great rejuvenation of the Chinese nation.

BackgroundRadiochromic GafChromic film models are widely used in clinical settings for quality assurance during cancer treatment planning. Although these films are extensively studied in photon dosimetry, research on their application in α‐particle dosimetry remains limited. With the growing use of α‐particles in cancer therapy, it is important to establish film dosimetry protocols tailored to α‐particles. Unlike photons, α‐particles are charged, have a high linear energy transfer, and induce significantly greater biological damage, highlighting the need for specialized dosimetric approaches.PurposeThis study aimed to evaluate the response of various unlaminated GafChromic film models including EBT3, EBT‐XD, and HD‐V2, irradiated with an 241Am α‐particle source, with combined experimental film irradiation and Monte Carlo (MC) simulations.MethodsIn this study, unlaminated EBT3, EBT‐XD, and HD‐V2 film pieces were irradiated with an 241Am disk source at various exposure times within a dark box. A detailed comparison was performed across the three film models, focusing on uncertainties and relative dose errors. Film analysis was conducted using a custom Python script, extracting normalized pixel values from the green channel. Additionally, a MC‐based user code was developed using the Geant4 simulation toolkit to model the 241Am source and calculate the dose rates in the active layers of the films and in water. The mean dose rates were also calculated in a 1 mm diameter region of interest. These simulated dose rates were employed to convert film exposure times into absorbed doses for both the active layers and water, establishing a reference dosimetry protocol for α‐particles across the three radiochromic GafChromic film models.ResultsThe mean dose rates within a 1 mm diameter circular region of interest in the active layers of the three unlaminated GafChromic film models were determined to be 3.77 ± 0.002 Gy/min for EBT3, 4.04 ± 0.0022 Gy/min for EBT‐XD, and 4.25 ± 0.0017 Gy/min for HD‐V2. When the film material was changed to water, the dose rate was increased 14.3% for EBT3, 19.2% for EBT‐XD, and 15.0% for HD‐V2, with EBT3 showing the closest match to water‐equivalence. Calibration curves for each film model were generated by fitting a power function to their responses. Refinements to the dose range were necessary to achieve an uncertainty below the 5% threshold. Among the models, HD‐V2 required the most adjustments to its dose range and exhibited the highest levels of experimental, fit, and total uncertainties, along with the largest relative dose errors.ConclusionsThis study investigated α‐particle dosimetry protocols for unlaminated EBT3, EBT‐XD, and HD‐V2 GafChromic film models using experimental irradiations and MC simulations. Although EBT3 and EBT‐XD demonstrate strong potential for α‐particle quality assurance in treatment planning, the HD‐V2 film model requires further investigation before it can be recommended for this application.

A three-parameter generalization of the Tsallis entropy based on the properties of the power functions and Weyl fractional calculus like extension of quantum calculus, are introduced. The generalization of the Shannon-Khinchin axioms corresponding to the fractional Tsallis entropy is verified and proposed. These axioms uniquely characterize new entropy function. For a certain sets of parameter values satisfied the second and third law of thermodynamics, the Lesche and thermodynamic stability criteria. PACS numbers: 05.50.+q, 05.70.-a, 05.90+m, 65.40.gd.

ABSTRACT In the study of vortex-induced vibrations (VIV) of marine risers, it is commonly assumed that ocean current in a single direction. However, in actual environments, ocean currents exhibit seasonal and periodic variations. This poses a challenge for the assessment of VIV fatigue damage. This paper establishes a assessment method for VIV fatigue damage in multidirectional current environments. A large number of cases are simulated to study the effects of multidirectional current parameters on fatigue. On this basis, the effects of various external and internal excitations are further analyzed. The results indicate that under various excitations, the maximum VIV fatigue damage is approximately related to the current velocity by a power function. Heave excitation significantly increases fatigue damage. The more pronounced the seasonal differences in the multidirectional current direction distribution, the smaller the maximum fatigue damage, and the more uniform the circumferential variation of fatigue damage along the riser.

Reinforced concrete structures in marine environments suffer from severe rebar corrosion. Basalt fiber reinforced polymer (BFRP) bars, which have better mechanical properties and corrosion resistance comparable to rebars, are a promising alternative. This study compares the durability of these two materials in concrete pore fluid simulating a marine environment. Through 0–100 days immersion experiments, it examines the mass and tensile property (tensile strength, elastic modulus, and ultimate strain) changes of the two types of bars, and uses the Arrhenius model, power function model, and exponential model to predict their long-term performance. Testing showed that after 100 days of immersion, BFRP bars had a mass loss rate of just 0.99%, compared to 3.83% for rebars. The minimum tensile strength retention rate of BFRP bars was 98.24%, versus 91.00% for rebars. The minimum elastic modulus retention rate of BFRP bars was 95.27%, while rebars only retained 92.25%. Thus, BFRP bars exhibited 7.24% and 3.02% higher tensile strength and elastic modulus retention rates, respectively, than rebars. Experimental results demonstrated that BFRP bars possess superior corrosion resistance to rebars in concrete pore fluids simulating a marine environment. Long-term predictions suggest BFRP bars last five times longer than rebars. This study shows that BFRP bars with excellent corrosion resistance and stable mechanical properties can replace rebars in marine concrete structures to effectively address corrosion issues.

ABSTRACT As modelling of nonlinear oscillator systems plays an important part in science and engineering fields, a double loop Radial Basis Function Neural Network (RBFNN) with adaptive radius and lattices is proposed for handling this issue. In this design, a large enough lattice arranged to cover all of the trajectories is taken as the mapping center of the RBFNN at the initial condition. The number of lattices will be dynamically adjusted, and those lattices far from the trajectories will be removed. Applying Taylor expansion in local space, the activated radius factor can be separated from the Gaussian function. In order to guarantee that the modelling scheme has the characteristic of fast convergence, the error power function is utilized to minimize the gain parameter of the error differential equation. In the double loop structure, the updated equation of weights and activated radius can be determined by the Lyapunov function, which can guarantee that the weights and the activated radius will converge to the neighborhood of their true value and the tracking error of state trajectories will converge to the neighborhood of zero. In order to show the effectiveness and superiority of the double loop RBFNN proposed in this paper, Helmholtz–Duffing and Vanderpol–Duffing are used as the testing objects of the nonlinear oscillator system while comparing with Deterministic Learning.

Emptying pressure pipelines is a routine operation during pipeline maintenance. This study investigates the emptying characteristics of pressurized pipelines with air valves under unsteady flow conditions. A mathematical model for the emptying process is developed using the rigid water column theory, exploring the influence of drain valve opening, initial air pocket length, and valve opening patterns on the transient flow behavior. The results indicate that, compared with the linear valve opening pattern, a nonlinear power function opening increases the minimum air pocket pressure head by 0.1014 m and delays its occurrence by 0.655 s. The maximum emptying velocity rises by 0.48 m/s when the opening is increased from 10% to 30%, thereby shortening the emptying time by 65.4%. However, the pressure head inside the air pocket decreases accordingly. When the air valve diameter is enlarged from 0.003 mm to 0.008 mm, the pressure recovery time is markedly reduced and the initial pressure fluctuations are attenuated. Numerical simulations based on the Heihe emptying case demonstrate that a well-planned layout of multiple air valves effectively shortens the duration of negative pressure heads. Replacing the first air valve with a 50 cm diameter circular orifice significantly raises the minimum pressure head of the pipeline and dramatically enhances the stability of emptying pressurized pipeline.

From structure to function: Biomechanical markers of symptomatic flatfoot during running and a single leg drop and hop.

Forests are ecologically complex, and trees play a structural and functional role in ecosystem dynamics. Tree height–DBH (diameter at breast height) relationships serve as a key indicator of forest productivity, competition, and succession, fundamental to sustainable forest management. This study develops height–DBH models for eight ecologically important tree species in boreal and mixed forests by applying nonlinear mixed-effects modelling approach to improve the predictive accuracy of height estimations. We evaluate height–DBH functions, including the two-parameter power function and Chapman–Richards function, incorporating stand-level variables—stand height based on dominant or co-dominant trees (SHT), basal area (BAH), and tree density (TPH) to refine predictions. Results indicate that mixed-effects models significantly improved model performance, with M4 (Chapman–Richards with mixed-effects) and M5 (Chapman–Richards function with mixed-effects and stand-level variables)–showing lowest AIC (Akaike Information Criterion) across species. Incorporating stand-level variables significantly enhanced performance, though improvements varied by species. The high accuracy of model M5 was further confirmed by validation process. Among stand-level variables, SHT contributed the most to height predictions (25.3 – 53.0%), while BAH (≤ 0.36%) and TPH (≤ 0.01%) had negligible effects. Still M4 can be a reliable alternative when stand-level variables are unavailable. This study highlights the effectiveness of a mixed-effects modelling framework complemented by stand-level variables in improving tree height estimation. Our research improves decision-making in growth and yield estimations of mixed stands and enhances the reliability of forest vegetation simulator outputs, thereby supporting ecological integrity.

Modeling lightness and brightness is a complex process since they are not simple functions of luminance, and they depend on additional properties of the stimulus and viewing conditions, as well as visual adaptation. Several XYZ-based metrics were developed to model lightness and brightness, which carry the disadvantages of the XYZ-based system. This study aims to develop one-dimensional brightness and lightness scales directly built based on cone fundamentals to account for the underlying physiology of the human visual system and individual differences. The proposed lightness and brightness scales are called FLS for Fundamental Lightness Scale and FBS for Fundamental Brightness Scale, respectively. The Helmholtz-Kohlrausch effect was included in using the G0 luminance the Bartleson-Breneman effect was modeled using an optimized power function, and the Stevens effect was included in using terminal brightness. Evaluation of the FLS and FBS scales was completed using seven data sets. In comparison to other models, the FLS and FBS have a good performance on all data sets.

ABSTRACT The modeling method of the Dou-Gong layer (DGL) is proposed and synergistic effect between multiple Dou-Gongs (DGs) is revealed in this study. DGL and DG have several interfaces and layers which are represented by hybrid elements, whereas the beam components (Fangs and Taojianliangs) are modelled with conventional beam elements. Then the beam-spring element model of the DGL is proposed based on those hybrid elements and beam elements. The iterative scheme for tackling nonlinear stiffness and horizontal displacement of DGL is also programmed based on this derived beam-spring element model. The compressive and shearing deformation behavior of the Mantousun in the DGL is revealed based on the solid element model. There is a nonlinear relationship between the lateral load borne by DGL and the sum of the lateral loads borne by DGs. The lateral loads applied in the Dou-Gong layer along the width and depth of a building are 5.76 times and 11.60 times that of the sum of eight Dou-Gongs, respectively, revealing the synergistic effect among multiple Dou-Gongs in the Dou-Gong layer. The lateral load-carrying capacity of DGL significantly improves with the increase of the cross-section area of DGL’s two components including Fang or Taojianliang, and they are in a power function relationship.

The spatial variability of soil shear wave velocity (Vs) significantly influences the results of site seismic response analysis. Based on the collected measured Vs values of silty clay in a certain sea area in China, this study divides the Vs data into one set of on-site sample data and six sets of historical data. A power function is used to establish the regression equation between Vs and depth h, and the joint prior distribution of the mean and variance for parameters a and b in the power function is derived using historical data. The joint posterior distribution of parameters a and b is obtained by applying the Bayesian formula to the on-site sample data. Using the maximum a posteriori mean values of a and b combined with the point estimation method, the mean and standard deviation of the predicted Vs values as functions of depth h are derived. The accuracy of the point estimation results is verified using Monte Carlo simulation. Compared to the Vs values predicted using only the mean values of a and b derived from on-site sample data, the Vs values predicted based on the maximum a posteriori mean values of a and b are closer to the measured Vs values. Accordingly, the results of the site seismic response analysis also align more closely with those calculated using the true Vs values.

Determinants of Kraus matrices associated with power functions

The growing urgency for transportation network development in seasonally frozen regions brings attention to two critical symmetrical factors: cyclic loading and freeze–thaw cycles. In saline soil areas, these symmetrical mechanical and environmental processes, along with varying salt content, significantly affect soil mechanical properties, posing considerable challenges for engineering design. In this study, the dynamic triaxial tests were conducted on a type of carbonate saline soil considering four factors, including moisture content, salt content, freeze–thaw cycle and confining pressure, and the variations in dynamic parameters, including dynamic strength and dynamic elastic modulus, with the above four factors were studied, and the influential mechanisms of four factors were fully discussed. The results demonstrated that the variations in dynamic strength (τd) versus vibration cycles (NF) were better fitted by logarithmic functions than by a linear one. An increase in moisture content, salt content, and freeze–thaw cycle all reduced the τd and dynamic elastic modulus (Ed); in addition, the Ed decreased significantly when the dynamic axial strain was less than 0.2%, and then stabilized with further increases in dynamic axial strain. The dynamic parameters of saline soil became nearly constant after undergoing five freeze–thaw cycles, and increased significantly with increasing confining pressure. Moreover, the relationship between the maximum dynamic elastic modulus (Edmax) and the four factors could be described by power functions. These findings could provide certain references for addressing the combined effects of symmetrical cyclic loading and freeze–thaw cycles in subgrade design for saline soil regions.