Normal Distribution Function Research Articles

Impact of bivariate Gaussian potentials on quantum walks for spatial search

Abstract Quantum search algorithms are crucial for exploring large solution spaces, but their robustness to environmental perturbations, such as noise or disorder, remains a critical challenge. We examine the impact of biased disorder potentials modeled by a bivariate Gaussian distribution function on the dynamics of quantum walks in spatial search problems. Building on the Ambainis-Kempe-Rivosh (AKR) model for searching on a two-dimensional grid, we incorporate potential fields to investigate how changes in standard deviation and normalization of the bivariate Gaussian function impact the performance of the search algorithm. Our results show that the quantum walk closely mirrors the AKR algorithm when the standard deviation is small but exhibits a rapid decay in success probability as the standard deviation increases.
This behavior demonstrates how the bivariate Gaussian can effectively model a noisy oracle within the AKR algorithm. Additionally, we compare the AKR-based model with an alternative quantum walk model using a Hadamard coin and standard shift. These findings contribute to understanding the robustness of quantum walk search algorithms, and provide insights into how quantum walks can be applied to optimization algorithms.

High detection rate of parasitic load by qPCR targeting 18S rDNA in blood of patients with active leishmaniasis lesions.

This study aimed to standardize qPCR techniques using these molecular markers kDNA and 18S rDNA across three sample types: peripheral blood, guanidine-treated blood, and tissue. The secondary objective is to evaluate the performance of 18S rDNA target in samples from 46 patients with confirmed tegumentary leishmaniasis. After obtaining the standard curve from reference strains with Leishmania, qPCR curves were standardizations and the Cts results of the patient samples were described using abstract measures. Specific specification equations (EEG) with normal distribution and identity link function were constructed to compare each type of clinical sample. To identify the differences among samples and techniques, multiple comparisons with Bonferroni post-test was performed. The kDNA and 18S rDNA demonstrated high sensitivity, detecting as few as 10⁻1 parasites/mL. However, 18S rDNA showed limited species discrimination. qPCR performance was evaluated using blood and tissue samples, showing a sensitivity of 54.2% in blood, 12.5% in guanidine-treated blood, and 86.4% in tissue. qPCR agreement with the 18S rDNA target with the three types of samples, positive and negative, in relation to screening were 56.2% in blood, 31.8% in guanidine- blood and tissue 78.6%. As for true positives (PPV), tissue samples presented a probability percentage of individuals being sick of 86.4%, while in blood it was 81.3%. The results underscore the importance of molecular diagnostics in blood samples, improving the accuracy and monitoring of tegumentary leishmaniasis.

The analysis of carrier transport mechanism at the interface of BZOPET-GR Schottky contact

Abstract Through the hydrothermal technique, we successfully deposited boron (B)-doped zinc oxide nanorods (ZnO NRs) onto a polyethylene terephthalate (PET)/graphene (GR) flexible substrate, creating a B-ZnO/PET/GR Schottky contact. The ZnO NRs exhibited a well-defined hexagonal structure with a lattice constant size of approximately 0.502 nm, as evidenced by characterization results. X-ray Photoelectron Spectroscopy (XPS) analysis revealed a reduction in defective oxygen content with increasing B ion doping.The current-voltage (I-V) characteristics of the Schottky contacts were systematically investigated over a temperature range of 160-300K. As the temperature increased, the barrier height exhibited an upward trend, while the ideality factor decreased. This behavior was ascribed to barrier inhomogeneity at the Schottky contact interface. Employing a single Gauss distribution function for barrier height, we verified and elucidated this phenomenon, contributing to a comprehensive understanding of the observed temperature-dependent electrical properties.

Experimental study of adhesion tension of wet coal dust and coal slurry

ABSTRACT The coal dusting process produces corrosive and adhesive coal slurry, which corrodes the surface of equipment and reduces its service life. To investigate the effect of velocity and water contents on the adhesion tension of wet coal dust and coal slurry, this paper experimentally measures the adhesion tension of wet coal dust and coal slurry in contact with metal surfaces. The results show that the trends of the adhesion pull and displacement relationship between wet coal dust and coal slurry are basically the same; the adhesion pull obtained by fast lifting is larger than that of slow lifting under the same water content, and the adhesion pull of coal slurry is larger than that of coal dust; the exponential decay function and the peak normal distribution function of adhesion pull are used to fit the change process of the adhesion pull and validate it. Through the validation experiments, we verify the two functions accuracy and reliability, which can provide expressions with high credibility for the prediction of the results of adhesion pull under the conditions of this experiment. Meanwhile, it also provides assistance for the selection and preparation of coal dust and coal slurry, which can help to improve the energy utilization and economic efficiency in the process of coal processing, conveying, and storage.

Generalized Gaussian Distribution Improved Permutation Entropy: A New Measure for Complex Time Series Analysis.

To enhance the performance of entropy algorithms in analyzing complex time series, generalized Gaussian distribution improved permutation entropy (GGDIPE) and its multiscale variant (MGGDIPE) are proposed in this paper. First, the generalized Gaussian distribution cumulative distribution function is employed for data normalization to enhance the algorithm's applicability across time series with diverse distributions. The algorithm further processes the normalized data using improved permutation entropy, which maintains both the absolute magnitude and temporal correlations of the signals, overcoming the equal value issue found in traditional permutation entropy (PE). Simulation results indicate that GGDIPE is less sensitive to parameter variations, exhibits strong noise resistance, accurately reveals the dynamic behavior of chaotic systems, and operates significantly faster than PE. Real-world data analysis shows that MGGDIPE provides markedly better separability for RR interval signals, EEG signals, bearing fault signals, and underwater acoustic signals compared to multiscale PE (MPE) and multiscale dispersion entropy (MDE). Notably, in underwater target recognition tasks, MGGDIPE achieves a classification accuracy of 97.5% across four types of acoustic signals, substantially surpassing the performance of MDE (70.5%) and MPE (62.5%). Thus, the proposed method demonstrates exceptional capability in processing complex time series.

Progressive development of soil arching and deformations in two- and three-dimensional trapdoor tests

In this study, two- and three-dimensional trapdoor tests were conducted using a newly developed trapdoor test device, to investigate the evolution of soil arching and fill deformation with different relative fill densities and fill heights. The test results show that the trapdoor settlements normalised by trapdoor width required for the soil arching ratios to reach minimum and ultimate values increased with fill height. In tests with dense fill, both the minimum and ultimate soil arching ratios were smaller compared to tests with loose fill at the same fill height. Two symmetrical slip surfaces developed from the trapdoor edges, with their inclination angles dependent on the dilatation angle of the sand. The proposed Gaussian distribution function with fitting parameters well matched the measured fill settlement profile. In the dense fill tests, the settlement trough’s width and volume loss induced by trapdoor settlement gradually decreased with fill elevation due to its strong shear dilation behaviour. Conversely, the loose fill exhibited weaker shear dilation behaviour, resulting in a larger settlement region. The settlement trough width and volume loss ratio, derived from the measured fill deformation, can be used to predict the fill deformation, including the surface settlement.

Stratospheric Transit Time Distributions Derived From Satellite Water Vapor Measurements

AbstractStratospheric transit time distributions (age‐of‐air spectra) are estimated using time series of satellite water vapor (H2O) measurements from the Microwave Limb Sounder over 2004 to 2021 assuming stationary transport. Latitude‐altitude dependent spectra are derived from correlations of interannual H2O anomalies with respect to the tropical tropopause source region, fitted with an inverse Gaussian distribution function. The reconstructions accurately capture interannual H2O variability in the “tropical pipe” and near‐global lower stratosphere, regions of relatively fast transport (∼1–2 years) in the Brewer‐Dobson circulation. The calculations provide novel observational estimates of the corresponding “short transit‐time” part of the age spectrum in these regions, including the mode. However, the H2O results do not constrain the longer transit‐time “tail” of the age spectra, and the mean age of air and spectral widths are systematically underestimated compared to other data. We compare observational results with parallel calculations applied to the WACCM chemistry‐climate model and the CLaMS chemistry‐transport model, and additionally evaluate the method in CLaMS by comparing with spectra from idealized pulse tracers. Because the age spectra accurately capture H2O interannual variations originating from the tropical tropopause, they can be used to identify “other” sources of variability in the lower stratosphere, and we use these calculations to quantify H2O anomalies in the Southern Hemisphere linked to the Australian New Years fires in early 2020 and the Hunga volcanic eruption in 2022.

A more holistic view of the logarithmic dose-response curve offers greater insights into insulin responses

The stimulus-response curve is usually modeled by the Hill function due to its simplicity and clear molecular mechanisms (Michaelis-Menten type of kinetics). Unfortunately, the mechanisms do not explain why the stimulus is ubiquitously measured by logarithmic dose rather than the dose itself and why the log(dose)-response curve possesses such fine properties as symmetry and wide adjustability. Here, the dose response is considered from a holistic perspective spanning multiple biological levels from molecules to the whole organism, which reveals that an appropriate model for log(dose) response is the cumulative normal distribution (CND) function, which had only statistical implication previously but now possess mechanistic-statistical duality. The present CND model establishes a connection between single-cell all-or-none responses and the graded response at the tissue/organism level, reveals the raison d'être of the logarithmic transformation, explains why log(dose)-response curve possesses many fine properties, and reveals new mechanisms of tissue/organism dose-response, including homogeneity-induced sensitivity. It also provides new insights into vital biological processes, such as the insulin dose response.

The Application of Information Theory to Interpret Shore Platform Erosion Rates

Advancements in information physics have recently introduced the application of information theory to investigate physical systems. The behaviour of erosion at the granular scale is to date still a complex system to unpack, and therefore geomorphology research requires novel approaches to better inform the interpretation of temporal and spatial erosion patterns at different scales. This paper applies information theory concepts to re-evaluate erosional data that were measured on limestone surfaces of two shore platforms in Malta with a traversing micro-erosion meter (TMEM). By representing erosion rates through their information content using a Box-Cox style transformation of the raw data (application of an inverse normal distribution function to fractionally ranked data), it is possible to identify points and measurement periods that contribute to a disproportionately large share of unexpected erosion rates that could provide more insight into the causes of erosion rates. Despite the variations in the information content from erosion rates at individual measurement points, most points consistently contribute to a similar amount of information. These findings illuminate the importance of considering the informational value of erosion data to further understand the underlying physical processes and potentially improve predictive models.

Modeling Water Clusters: Spectral Analyses, Gaussian Distribution, and Linear Function during Time

Our experimental and theoretical studies have consistently revealed the presence of water clusters in various environments, particularly under hydrophobic conditions, where slower hydrogen ion interactions prevail. Crucial methods like Nuclear Magnetic Resonance (NMR) and Fourier Transform Infrared (FTIR) method have played a pivotal role in our understanding of these clusters, unveiling their potential medical applications. The stability and behavior of these clusters can be influenced by factors such as metal ions’ presence, leading to stable clusters’ formation. This potential for medical applications should inspire hope and further research. Moreover, our research has revealed that water clusters exhibit characteristics of dissipative structures, demonstrating the self-organization under physical, chemical, or thermal changes akin to Rayleigh–Benard convection cells. This dynamic and significant behavior supports the notion that water’s role transcends simple chemistry, potentially influencing biological processes at a fundamental level. The interaction of water clusters with their environment and the ability to maintain non-equilibrium states through the energy exchanges further underscores their complexity and significance in both natural and technological contexts. Water filtration is a process for improving water quality. The effect is re-structuring hydrogen bonds and structuring water clusters, most of which are hexagonal. In our research, we applied filtered water using patented EVOdrop Swiss technology.

A prediction method of oil recovery for hot water chemical flooding in heavy oil reservoirs: Semi-analytical stream tube model

Abstract Chemical agents (polymer and surfactant) assisted hot water flooding is an effective means of enhancing oil recovery in heterogeneous and heavy oil reservoirs. The rapid prediction of oil recovery through hot water chemical flooding is very important. The stream tube model is a fast analytical method for predicting water flooding recovery, but it is not suitable for hot water chemical flooding. In this paper, a permeability distribution model for multi-stream tubes is established based on permeability variation coefficient using normal distribution function for reservoir heterogeneity, Using GOMPERTZ growth function model to characterize the changes in stream tube temperature, polymer viscosity, and surfactant concentration with injection volume, Using Brooks-Corey model to describe the influence of interfacial tension and temperature on the relative permeability curve. Finally, an analytical stream tube model for hot water chemical flooding of heavy oil reservoirs was established. The time discrete method is used to solve the model, then the graphs of the relationship between oil recovery and water cut are obtained. Compared with numerical simulation methods, the prediction error of oil recovery is less than 2%, and the calculation time is reduced by 89%. This model has been successfully applied to X oilfield. Based on historical fitting, it is predicted that hot water chemical flooding can enhance oil recovery by 6.3% compared to water flooding. This paper provides a fast calculation method for predicting and evaluating the effectiveness of hot water chemical flooding in heavy oil reservoirs.

Cytokine trajectory over time in men and women with HIV on long-term antiretroviral therapy.

Although antiretroviral therapy (ART) suppresses viral replication and reduces inflammation, it does not lead to the normalization of cytokines. The long-term effects of ART beyond viral suppression have not been studied and are mostly limited to cross-sectional research. The impact of long-term ART on the trajectory of 40 cytokines/chemokines in 31 men and 59 women who maintained viral suppression over a median period of 6 years (317 visits ranging from 24 to 384 weeks post ART initiation) were measured by Luminex. We used a generalized additive model with a Gaussian distribution and identity link function to model concentrations over time and investigate sex and race differences. While most cytokine/chemokine trajectories remained stable, the trajectory of nine markers of monocyte/macrophage activation (IP-10, I-TAC, MIG, sCD163, sCD14, MCP-1, MIP-3β, CXCL13, TNF-α) decreased over time (adj. P < 0.05). Despite continuous viral suppression, M-CSF, IL-15, and LBP increased over time (adj. P < 0.05). sCD14 was the only cytokine whose trajectory differed by sex (adj. P = 0.033). Overall, women had lower mean levels of IL-18 but higher levels of sCD14 than did men (adj. P < 0.05). GROα, LBP, and sCD14 showed significant differences between races (adj. P < 0.05). No association between cytokines and cellular HIV DNA/RNA was found. Our study reveals a continuous decline in markers of monocyte/macrophage activation over 6 years of suppressive ART, indicating that long-term treatment may mitigate inflammaging and cardiovascular-related outcomes. The higher levels of sCD14 observed in women are consistent with them having greater innate immune activation than men do.

Seismic scattering inversion for multiple parameters of overburden-stressed isotropic media

Subsurface reservoirs are compressed by overburden stress resulting from the gravity of overlying masses, and the resulting stress changes significantly affect the seismic reflection responses generated at the reservoir interfaces. Several exact reflection coefficient equations have been well established to delineate the role that in situ stress plays in altering the energy transition and amplitude of seismic reflection responses. These exact equations, however, cannot be effectively used in practice due to their intricate formulations and the difficult geophysical estimation for the third-order elastic constants (3oECs) embedded in reflection coefficients. Based on the theories of nonlinear elasticity and elastic wave inverse scattering, we derive an approximate seismic reflection coefficient equation for overburden-stressed isotropic media in terms of the P-wave modulus, shear modulus, density, and a defined stress-related parameter (SRP). The SRP is a combined quantity of elastic moduli, 3oECs, and overburden stress, which can be naturally treated as a dimensionless stress-induced anisotropy parameter. Its inclusion effectively eliminates the need for 3oECs information when using our equation to estimate the desired reservoir properties from seismic observations. By comparing our equation to the exact one, we confirm its validity within the moderate-stress range. Then, we introduce a Bayesian inversion approach incorporating the new reflection coefficient equation to estimate four model parameters. In our approach, the Cauchy and Gaussian distribution functions are used for the a priori probability and the likelihood distributions, respectively. The synthetic tests from two well-log data sets and a field example demonstrate that four parameters can be reasonably inverted using our approach with rather smooth initial models, which illustrates the feasibility of our inversion approach.

Semi-supervised action recognition with dynamic temporal information fusion

The most advanced semi-supervised models available are based on images for innovation, and the use of semi-supervised learning models augmented with temporal data for video-level action recognition still suffers from severe model mismatches, and the models are not sufficiently capable of capturing both local and global information about the action. Secondly the use of constant-threshold pseudo-labeling leads to low utilization of unlabeled data for difficult actions in the early stages of training, poor pseudo-labeling quality and affects recognition accuracy. To make the semi-supervised framework FixMatch more suitable for action recognition, we propose Time-Mixer and Dynamic Threshold, respectively. Time-Mixer explores complementary information between time sequences through the fusion of two-channel temporal context information. Dynamic Threshold utilizes a new core mapping function (Normal Distribution Function) to enhance pseudo-labeling quality. Extensive experiments were conducted on three action recognition datasets (Kinetics-400, UCF-101, and HMDB-51). Comprehensive experiments show that the performance of the semi-supervised model in action recognition improves considerably after using dynamic thresholding and temporal context information fusion, with a 14.4% improvement over the baseline and a 1.8% improvement over the TG (with a labeling rate of 10%) in UCF101, whereas an overall good performance is obtained for DTIF.

Выбор функции зависимости вероятности появления остаточных деформаций от нагрузок при определении оптимальных возвышений наружного рельса в кривом участке пути

Purpose: the outer rail elevation in a curved section of railroad track according to the 2021 Guide for Determining the Elevation of the Outer Rail is determined by taking into account unmitigated accelerations, radii (permissible and admissible). Taking these indicators into account allows to determine the best values of outer rail elevations in terms of operational characteristics. But these elevations cannot be called optimal in terms of the amount of work performed during the current maintenance of the track in curves. To determine the optimal elevation, labor costs should be considered throughout the life cycle of the curved section. Since the occurrence of costs is mainly influenced by residual deformations during the life cycle, it was decided to consider the probability of residual deformations during the life cycle. Methods: the choice of the function of dependence of the probability of occurrence of residual deformations on loads was made on the basis o probability theory and regression analysis. The least squares method was used as a method of regression analysis. On its basis, functions with the greatest convergence relative to the function obtained using probability theory were selected. Results: the study found that dynamic loads generated during rolling stock movement on railway tracks follow a normal distribution function according to probability theory. Since certain dynamic loads during operation lead to residual deformations, the probability of such deformations can also be described using a normal distribution function. The resulting function for predicting the probability of residual deformations based on load factors was identified. Practical significance: the research findings can be used to determine the optimal elevation of the outer rail that minimizes labor costs during railway track operation

Characterization of Hydraulic Spool Clamping Triggered by Solid Particles Based on Mechanical Model and Experiment Research

Hydraulic spool valves may clamp under the action of sensitive particles when working in hydraulic oils that contain solid particles, which will then bring about a devastating detriment to the machines. According to the failure statistics of hydraulic systems organized by ISO, more than 80% of the operational failures of hydraulic systems are caused by fluid contamination, and particulate contamination is the most important factor causing spool valve stagnation. In this paper, we considered various factors, including the material, size, and concentration of particles and the spool postures, and built a systematic spool clamping mechanical model. A device was designed to measure the spool valve friction under the action of particles. The influence of particle material, concentration, and size on the friction force of spool valves was investigated. By experiments, we measured the spool clamping force under the action of each single factor and then fitted the datum quantity of spool clamping force and the empirical equation of pulsating quantity. The study results demonstrate three types of non-ideal postures of spools in a valve hole, which are off-center, tilting, and off-center with tilting. Those three postures can engender clamping risk zones with different ranges inside the clearance between spool valves, increasing the risk of spool clamping. The kind of particles is found to have a certain but limited impact on the spool clamping force. Usually, particles with a higher elastic modulus can trigger a larger spool clamping force, which is in line with the theoretical equation. Within a certain range, the probability density distribution of particle size tallies with the normal distribution function, where the “sensitive particles” take up 0.7–1 of the clearance between spool valves. A higher particle volume fraction in oils means a greater number of sensitive particles and a larger spool clamping force. For the particles of a similar size with the clearance between spool valves, when their volume concentration tops over the “sensitive concentration”, namely 5%, the risk of spool clamping rises in a drastic manner. This study provides a theoretical reference and an empirical equation for the mechanism of spool clamping under the action of particles, as well as a definite quantitative indicator for the prediction and estimation of spool clamping which is of positive significance for the study of the predictive maintenance of hydraulic equipment.

Статистический анализ изменения температуры воздуха по данным многолетних наблюдений Метеорологической обсерватории имени В. А. Михельсона РГАУ – МСХА

Introduction. The purpose of the study is to assess the dynamics of changes in air temperature indicators and its impact on agronomic systems, based on long-term observations of the V. A. Mikhelson Meteorological Observatory of RSAU – MTAA. Materials and Methods. Using the Mathcad program, graphs of changes in average annual temperatures were constructed using a third-order approximation polynomial, graphs of the theoretical normal density distribution and normal temperature distribution function, as well as graphs of intra-annual temperature distribution for 30 years. Research results and Discussion. The values of the relative error of average annual temperatures were calculated, the normal distribution of average annual temperatures was checked using the Pearson criterion, after which the probability of deviation of the empirical hours falling into intervals from the theoretical hours was found. Conclusion. As a result of the research, a significant increase in average annual air temperature was established against the background of a general reduction in the duration of the cold period. Increase in temperature over the period 1961–1990 amounted to 0.9 °C, which is significantly higher than the average values for the globe. The results of the study reflect the general trend of warming in the context of global climate change and can be used to improve the forecasting of weather conditions, as well as to optimize technological processes in crop production.

Effect of preload scatter on fatigue life of subsea pipeline connector bolts located at suspended span section

The subsea pipeline connector (SPC) located at suspended span section not only bears the internal pressure from the oil and nature gas of the pipeline, but also needs to withstand the periodic drag force generated by vortex-induced vibration (VIV). This situation may cause fatigue failure of the flange connector fastening bolts. Reasonable preload value can reduce the fatigue stress and improve the fatigue life of the SPC bolts. This paper establishes a calculation model of the SPC drag force under VIV located at suspended span section. Normal distribution function is used to establish random models of preload for corner control pretension method and hydraulic tension pretension method considering the scatter of the preload value. On this basis, the stochastic finite element model (S-FEM) of SPC bolts is established to analyze bolts force under random preload considering VIV. The regression equation of strain-life for smooth fatigue specimens of bolt materials is applied to obtain preload-fatigue life curves of SPC bolts under different pretension methods. Then it is used to analyze the preload scatter on fatigue life of SPC bolts located at suspended span section. The analysis results indicate that the fatigue life dispersion of SPC bolts pre tightened by hydraulic tension pretension method is smaller compared with the corner control pretension method. Compared with the preload value determined by ASME code, increasing the SPC bolts preload appropriately can improve the fatigue life of SPC fastening bolts located at suspended span section.

Study on the Extension of Critical Zones Along Tunnel Alignments and Its Impact on Structural Damage to Nearby Buildings

When tunnelling in urban environment, tunnels are unavoidably excavated in close proximity of neighbouring buildings. It is inevitable that tunnels will interact with building foundations and other existing infrastructures. Consequently, ground movements produced by tunnel works and namely settlement, can cause serious damage to existing buildings. The objective of this study is to investigate the critical area in terms of ground movements produced by tunnelling by using the gaussian distribution function which is the most famous approach used in practice engineering for studying settlements induced by tunnel excavation, combined with conventional damage risk assessment approach based on limit value of highest settlement.

Central Limit Theorem and Law of Large Numbers Analogues for the Total Progeny in the Q-Processes

In this paper we are dealing with population size growth systems called Q-processes. The class of trajectories of these systems is a subset of the family of all possible trajectories of the ordinary Galton-Watson branching system, provided that they do not decay in the remote future. We observe the total progeny of a single founder-individual, generated by the reproduction law of the Q-process up to time n. By analogy with branching systems models, this variable is of great interest in studying the deep properties of the Q-process. Our main results are analogues of Central Limit Theorem and Law of Large Numbers for Sn, denoting the total progeny of a single founder-individual, generated by the reproduction law of the Q-process up to time n. We find that the total progeny as a random variable approximates the standard normal distribution function under a second moment assumption for the initial Galton-Watson system offspring law. We estimate the speed rate of this approximation. We also prove an analogue of the law of large numbers with an estimate of the approximation rate to the degenerate distribution.