Classical Techniques Research Articles

Precision and efficiency of an interpolation approach to weakly singular integral equations

PurposeThis study aims to discuss the numerical solutions of weakly singular Volterra and Fredholm integral equations, which are used to model the problems like heat conduction in engineering and the electrostatic potential theory, using the modified Lagrange polynomial interpolation technique combined with the biconjugate gradient stabilized method (BiCGSTAB). The framework for the existence of the unique solutions of the integral equations is provided in the context of the Banach contraction principle and Bielecki norm.Design/methodology/approachThe authors have applied the modified Lagrange polynomial method to approximate the numerical solutions of the second kind of weakly singular Volterra and Fredholm integral equations.FindingsApproaching the interpolation of the unknown function using the aforementioned method generates an algebraic system of equations that is solved by an appropriate classical technique. Furthermore, some theorems concerning the convergence of the method and error estimation are proved. Some numerical examples are provided which attest to the application, effectiveness and reliability of the method. Compared to the Fredholm integral equations of weakly singular type, the current technique works better for the Volterra integral equations of weakly singular type. Furthermore, illustrative examples and comparisons are provided to show the approach’s validity and practicality, which demonstrates that the present method works well in contrast to the referenced method. The computations were performed by MATLAB software.Research limitations/implicationsThe convergence of these methods is dependent on the smoothness of the solution, it is challenging to find the solution and approximate it computationally in various applications modelled by integral equations of non-smooth kernels. Traditional analytical techniques, such as projection methods, do not work well in these cases since the produced linear system is unconditioned and hard to address. Also, proving the convergence and estimating error might be difficult. They are frequently also expensive to implement.Practical implicationsThere is a great need for fast, user-friendly numerical techniques for these types of equations. In addition, polynomials are the most frequently used mathematical tools because of their ease of expression, quick computation on modern computers and simple to define. As a result, they made substantial contributions for many years to the theories and analysis like approximation and numerical, respectively.Social implicationsThis work presents a useful method for handling weakly singular integral equations without involving any process of change of variables to eliminate the singularity of the solution.Originality/valueTo the best of the authors’ knowledge, the authors claim the originality and effectiveness of their work, highlighting its successful application in addressing weakly singular Volterra and Fredholm integral equations for the first time. Importantly, the approach acknowledges and preserves the possible singularity of the solution, a novel aspect yet to be explored by researchers in the field.

Extracting indicators of connectedness to nature to improve water conservation behavior in agriculture

To better understand the connection between humans and nature, as well as why destructive behaviors occur that have led to drastic environmental changes, it is important to understanding determine the factors affecting this relationship, as well as extension and strengthening pro-environmentalist attitudes and behaviors in relation to nature can to provide appropriate solutions to the climate crisis. In this regard, it is very important to pay attention to human behavior in agriculture and water resources management. The purpose of the research was to extract indicators of connectedness to nature (CTN) in order to improve water conservation behavior (WCB) in the agriculture sector. To achieve this goal, the classic Delphi technique was used to get experts' opinions. The statistical population of this study was 20 subject matter experts in the fields of agricultural extension and education, environment and water resources, who were selected in a purposeful way. The results included the extraction of 140 indicators in the first stage of Delphi, and in the final stage, 100 indicators were confirmed and finalized. These indicators are in the form of CTN components (including cognitive, affective and behavioral dimensions), WCB, water conservation environmental values (including egoistic, altruistic and biospheric attitudes), environmental norms (including subjective and social norms), water conservation beliefs, environmental concern, empathy with nature, mindfulness, place attachment, place identity and environmental identity were divided. The obtained indicators can be used by policy makers and decision makers to evaluate the concept of CTN in relation to WCB in the agriculture sector.

A robust alternative to the Lilliefors test of normality

The Lilliefors test of normality is a popular and easy-to-explain method for testing whether a sample comes from a normal distribution. Unfortunately, since it relies on the sample mean and sample standard deviation for estimating the parameters of the normal distribution, the Lilliefors test is quite sensitive to the presence of outliers. Contrarily to what could be expected, the substitution of the estimators of location and scale by robust alternatives still does not suffice for obtaining a robust method when either the number of outliers or the sample size is large. In this paper, we propose an actual robust alternative relying on classical and data-driven trimming techniques. The presented test depends on the choice of a subsetting technique, of which we explore three possibilities, and of one parameter, which models the robustness of the test in the presence of outliers. As expected, the choice of parameter is a delicate issue since the gain in robustness comes at the price of a reduced power against some types of alternatives.

Graft Reorientation and Lateral Extra-articular Tenodesis in Revision Surgery for Persistent Rotational Instability of a Verticalized Anterior Cruciate Ligament Graft

Persistent rotational instability after anterior cruciate ligament reconstruction is a relatively common postoperative complication, typically associated with graft verticalization due to improper femoral tunnel placement, especially with classic transtibial femoral tunnel techniques. This article describes a technique designed to reorient a verticalized anterior cruciate ligament graft at its femoral insertion to a more anatomic position in the coronal and sagittal planes, aiming to restore knee stability without the need for a complete revision operation. Additionally, a lateral extra-articular tenodesis with fascia lata is added to reinforce rotational stability.

Modeling and Analysis of an Age-Structured Malaria Model in the Sense of Atangana–Baleanu Fractional Operators

In this paper, integer- and fractional-order models are discussed to investigate the dynamics of malaria in a human host with a varied age distribution. A system of differential equation model with five human state variables and two mosquito state variables was examined. Preschool-age (0–5) and young-age individuals make up our model’s division of the human population. We investigated the existence of an area in which the model is both mathematically and epidemiologically well posed. According to the findings of our mathematical research, the disease-free equilibrium exists whenever the fundamental reproduction number R0 is smaller than one and is asymptotically stable. The disease-free equilibrium point is unstable when R0>1. We showed that the endemic equilibrium point is unique for R0>1. Also, the most influential control parameters of the spread of malaria were identified. Numerical simulations of both classical and fractional order were conducted, and we used ODE (45) for classical part and numerical technique developed by Toufik and Atangana for fractional order. The infected population will grow because of the high biting frequency of the mosquito and the high likelihood of transmission from the infected mosquito to the susceptible human. R=1.622, which is more than one, indicating that the mosquito vector keeps on growing. This supports the stability of the endemic equilibrium point theorem, which states that the disease becomes endemic when R=1. The susceptible human population will decrease because of the presence of the infective mosquito, which has a high biting frequency for the first couple of days. Since the infective mosquito bit the susceptible human, the susceptible human became infected and went to the infected human compartments. Then, the susceptible population will decrease and the infested human population will increase. After a certain amount of time, it becomes zero due to the growth of protected classes. In this case, a disease-free equilibrium point exists and is stable. This condition exists because R0=2.827×10−5 is less than 1. This supports the theorem that the stability of the disease-free equilibrium point is obtained when R0<1. Depending on equation, we have shown that the possibility of some endemic equilibria exists when R0<1, that is, it undergoes backward bifurcation, even when the disease-free equilibrium is locally stable, and the result means that the society may misunderstand the level of malaria prevalence in the community.

An efficient method for generalised Wiener series estimation of nonlinear systems using Gaussian processes

System identification of dynamical systems aims to predict the output of a system for a given input by inferring model details from data. This is particularly challenging for nonlinear vibrating systems with long memory, which often have complex dynamics for which the physics is not fully understood. However, in many engineering applications, it is important to capture as much of the nonlinearity in the response as possible. The Wiener series is a classical data-driven technique that decomposes the system response into a set of orthogonal functionals of increasing order. Unlike standard black-box algorithms, such as neural networks, the series is highly interpretable and can offer insight into the nonlinearities present. However, current methods require vast quantities of data to calculate higher order terms in the Wiener series. In this paper, a novel generalised formulation of the Wiener series is developed by framing the series explicitly as a QR decomposition. Then by placing a Gaussian process prior over the kernels, their inherent structure is exploited to significantly reduce the quantity of data required for inference. Initial investigations were carried out using two systems: first pre-defined kernels and second an idealised nonlinear oscillatory system with unknown kernels. It is demonstrated that the Gaussian Process Generalised Wiener Series (GPGWS) enables the calculation of up to and including the third order kernel for systems with long memory and improves the robustness to noise.

A Comparative Analysis of IoT based Network Anomaly Detection and Prediction Using Vector Autoregressive Models

This research provides a comparative analysis of the use of Vector Autoregressive models for network anomaly detection and prediction. It starts by giving a brief overview of the models and going over the two versions that are available for network anomaly detection. Ultimately, the study offers an empirical assessment of the two types of models, just considering how well they detect and forecast anomalies overall. The results show that the unmarried-node anomaly detection performance of the model is superior. Simultaneously, the Adaptive Learning version is particularly effective in identifying anomalies among a few nodes. The fundamental reasons for the differences in the two fashions' overall performance are also examined in this research. This work provides a comparative analysis of two widely utilized algorithmic approaches: vector autoregressive models and community anomaly detection and prediction. Each method's effectiveness is assessed using two different network datasets: one based on real-world global measurements of latency and mobility ranges, and the other focused on a fictional community. The study also examines the trade-offs between employing the versus other modern and classic techniques, Markov Chain Monte Carlo, and Artificial Neural Networks for network anomaly detection. Finally, it provides an overview of the advantages and disadvantages of each technique as well as suggestions for improving performance.

Reinforcement learning approaches for the stochastic discrete lot-sizing problem on parallel machines

This paper addresses the stochastic discrete lot-sizing problem on parallel machines, which is a computationally challenging problem also for relatively small instances. We propose two heuristics to deal with it by leveraging reinforcement learning. In particular, we propose a technique based on approximate value iteration around post-decision state variables and one based on multi-agent reinforcement learning. We compare these two approaches with other reinforcement learning methods and more classical solution techniques, showing their effectiveness in addressing realistic size instances.

Asymptotic distribution of the zeros of a certain family of generalized hypergeometric polynomials

The primary aim of this paper is to investigate the asymptotic distribution of the zeros of certain classes of hypergeometric q + 1 F q polynomials. We employ classical analytical techniques, including Watson's lemma and the method of steepest descent, to understand the asymptotic behavior of these polynomials: q + 1 F q ( − n , kn + α , … , kn + α + q − 1 q ; kn + β , … , kn + β + q − 1 q ; z ) ( n → ∞ ) , where n is a nonnegative integer, q is a positive integer and the constant parameters α and β are constrained by α < β . By applying the general results established in this paper, we generate numerical evidence and graphical illustrations using Mathematica to show the clustering of zeros on certain curves.

A comparative study of variational autoencoders, normalizing flows, and score-based diffusion models for electrical impedance tomography

Abstract Electrical Impedance Tomography (EIT) is a widely employed imaging technique in industrial inspection, geophysical prospecting, and medical imaging. However, the inherent nonlinearity and ill-posedness of EIT image reconstruction present challenges for classical regularization techniques, such as the critical selection of regularization terms and the lack of prior knowledge. Deep generative models (DGMs) have been shown to play a crucial role in learning implicit regularizers and prior knowledge. This study aims to investigate the potential of three DGMs – variational autoencoder networks, normalizing flow, and score-based diffusion model – to learn implicit regularizers in learning-based EIT imaging. We first introduce background information on EIT imaging and its inverse problem formulation. Next, we propose three algorithms for performing EIT inverse problems based on corresponding DGMs. Finally, we present numerical and visual experiments, which reveal that (1) no single method consistently outperforms the others across all settings, and (2) when reconstructing an object with two anomalies using a well-trained model based on a training dataset containing four anomalies, the conditional normalizing flow (CNF) model exhibits the best generalization in low-level noise, while the conditional score-based diffusion model (CSD*) demonstrates the best generalization in high-level noise settings. We hope our preliminary efforts will encourage other researchers to assess their DGMs in EIT and other nonlinear inverse problems.

Does routine partial lateral sphincterotomy with open hemorrhoidectomy improve postoperative pain?

Objective In this study we aimed to detect the difference regarding the postoperative pain and continence in patients with third and fourth degree hemorrhoidal disease who underwent either hemorrhoidectomy alone or combined hemorrhoidectomy with partial internal sphincterotomy for the treatment of hemorrhoidal disease. Patients and methods This prospective comparative randomized clinical trial was conducted at hospitals of Tanta University during the period from March 2021 to August 2022 on 100 patients with third or fourth degree hemorrhoids who were randomly assigned either to group A, patients who only underwent hemorrhoidal excision by the classical technique of Milligan–Morgan or group B, with added partial lateral sphincterotomy to the classic technique. All patients in both groups underwent anorectal manometry both preoperatively and postoperatively. Pain following surgery was analyzed by using visual analog scale system at 24 h, 48 h, and on 10th postoperative day, other complications including incontinence, infection, hematoma, bleeding, and anal stricture were evaluated at 24 h, 48 h, 10th postoperative day, 1 month, and after 3 months. Results Total 100 patients were divided among both groups. The mean age of the patients was 37.7±11.3 and 36.3±11.3 years in group A and group B, respectively. Thirty-two males and 18 females were in group A in comparison to 33 males and 17 females in group B. During follow-up periods, patients in group B had less postoperative pain than those in group A with statistically significant difference. None of the patients developed fecal incontinence for solid or liquid stools in both groups, except for nine patients developed only mild degree of incontinence for flatus in the first week that improved gradually till completely resolved before the end of the 3 months follow up. Conclusion The addition of partial internal sphincterotomy to the classical haemorrhoidectomy technique significantly improves postoperative pain without increasing overall related morbidity.

Preoperative 3D Microvascular Decompression Simulation

Preoperative surgical simulation via three-dimensional fusion computer graphics models have been widely accepted as a legitimate means of securing the diagnosis and treatment effectiveness of neurovascular compression. The authors discussed three factors of surgical simulation as being 1. Knowing the anatomical relationship, 2. Knowing the desirable end result of surgical intervention, and 3. Knowing how to design surgical interventions to achieve such desirable end results. Satisfying each factor requires distinct functionality from the software used in the surgical simulation. As per the imaging study used to construct the multimodal computer graphic models, CT scan and MR are usually sufficient, although renal function-permitting contrast enhancement can be a feasible option for depicting minute vessels in particular. There are three major steps in building three-dimensional fusion computer graphics models:1. Image interpretation, 2. co-registration, and 3. Segmentation. Each step comprises an essential part that must be handled with care. The segmentation step is where rigorous technological advancement takes place, although classical techniques, such as the seeded region growing method or the multi-threshold method, are still practically important. Regarding surgical simulation after three-dimensional model construction, technical challenges concerning large deformations should be recognized to ensure non-nonsense surgical simulation.

Microfluidic approaches in microbial ecology.

Microbial life is at the heart of many diverse environments and regulates most natural processes, from the functioning of animal organs to the cycling of global carbon. Yet, the study of microbial ecology is often limited by challenges in visualizing microbial processes and replicating the environmental conditions under which they unfold. Microfluidics operates at the characteristic scale at which microorganisms live and perform their functions, thus allowing for the observation and quantification of behaviors such as growth, motility, and responses to external cues, often with greater detail than classical techniques. By enabling a high degree of control in space and time of environmental conditions such as nutrient gradients, pH levels, and fluid flow patterns, microfluidics further provides the opportunity to study microbial processes in conditions that mimic the natural settings harboring microbial life. In this review, we describe how recent applications of microfluidic systems to microbial ecology have enriched our understanding of microbial life and microbial communities. We highlight discoveries enabled by microfluidic approaches ranging from single-cell behaviors to the functioning of multi-cellular communities, and we indicate potential future opportunities to use microfluidics to further advance our understanding of microbial processes and their implications.

Towards Codebook-Free Deep Probabilistic Quantization for Image Retrieval.

As a classical feature compression technique, quantization is usually coupled with inverted indices for scalable image retrieval. Most quantization methods explicitly divide feature space into Voronoi cells, and quantize feature vectors in each cell into the centroids learned from data distribution. However, Voronoi decomposition is difficult to achieve discriminative space partition for semantic image retrieval. In this paper, we explore semantic-aware feature space partition by deep neural network instead of Voronoi cells. To this end, we propose a new deep probabilistic quantization method, abbreviated as DeepIndex, which constructs inverted indices without explicit centroid learning. In our method, the deep neural network takes an image as input and outputs its probability of being put into each inverted index list. During training, we progressively quantize each image into the inverted lists with the top- T maximal probabilities, and calculate the reward of each trial based on retrieval accuracy. We optimize the deep neural network to maximize the probability of the inverted list with maximal reward. In this way, the retrieval performance is directly optimized, leading to a more semantically discriminative space partition than other quantization methods. The experiments on public image datasets demonstrate the effectiveness of our DeepIndex method on semantic image retrieval.

Chemical Correlation of Cistendiol Obtained from Cativic Acid in Two Different Pathways

Objective This study aims to convert cativic acid, which was isolated from Ageratina jocotepecana, into cistendiol (5), an analog of cistenolic acid isolated from Cistus symphytifolius. The position of hydroxyl at C-7 in compound 5 could be achieved by applying the Schenck reaction with singlet oxygen (1O2) through photooxidation reaction of 6. Additionally, epoxidation reaction of 1, followed by further reduction and acid treatment, can serve as another pathway to obtain compound 5. Methods Cativic acid was isolated from Ageratina jocotepecana flowers, reduction methodology was realized with THF and LiAlH4, epoxidation reaction was carried out with mCPBA in CH2Cl2 and K2CO3, oxidation of alcohol with PCC in CH2Cl2 and MgSO4, photooxidation reaction was realized with blue and white light using singlet oxygen (1O2) and photosensitizers such as eosin, methylene blue and Ru(bpy)3(PF6)2 in acetonitrile. Geometry optimizations for transition states were performed using MMFF94 with Monte Carlo protocol, and GDFT was used B3LYP/DGDZVP level of theory with Gaussian 09. Results Cistendiol was synthesized by photooxidation reaction of 6 with Ru(bpy)3(PF6)2 and air such oxidant with a ratio of 8:1, while epoxidation of 1 further reduction and acid treatment afforded cistendiol with a ratio of 9:1, the ratio was determined by NMR, additionally the global minimum energy structures GDFT calculated values supports the results described by NMR ratio. The stereochemistry was also confirmed by NOESY experiment and the comparison is in agreement with literature data. Conclusion Herein, we described the conversion of cativic acid isolated from Ageratina jocotepecana employing a new photooxidation methodology and classic epoxidation techniques, to produce an analog of cistenolic acid isolated from Cistus symphytifolius. The results, which include Supplemental material, enable comparison of stereochemistry, specifically the 13 S for C-13 of Ageratina jocotepecana with other compounds such as cistenolic or salvic acid, which had been the subject of study by researchers.

Detection of Resistance, Susceptibility, Tolerance, and Virulence in Plant-Nematode Interactions: Part I-Sedentary Endoparasitic Nematodes.

The use of nonhost, tolerant, or resistant plants, to manage plant parasitic nematodes (PPNs), is an appealing, economic, and environmentally friendly agronomic practice, which is effective when precise information on the identification of PPN species and their virulence to target host crops is available. This chapter describes suggested protocols to evaluate the reaction of the most important crops and fruit trees to infestation by the most damaging PPN with sedentary endoparasitic habits, with the aim of assessing resistance and tolerance traits, sources of resistance in progenies from breeding programs, the reaction to nematodes of newly released cultivars, and the virulence of the most noxious PPNs. These protocols consist of classical screening techniques not involving biochemical and molecular analyses. PPN species and genera considered in this chapter include (i) the most importantspecies of root-knot nematodes Meloidogyne spp., including alsoM. chitwoodi, M. enterolobii, and M. graminicola, and (ii) the cyst-forming nematodes of the genera Globodera and Heterodera, such as the potato cyst nematodes (PCNs) Globodera rostochiensis and G. pallida, and also Heterodera avenae group, H. ciceri, H. glycines, and H. schachtii. Schemes are given to identify virulence groups for most of these nematodes.

An Information Fusion Technique for Prognosticating Future Air Passenger Trends

The aviation industry is constantly changing and to keep up with the trends of air passengers we need predictive models. In this paper, we explore the use of Information Fusion methodologies and classical time series techniques to forecast how many passengers will be traveling by air. Predicting passenger demands is a task, due to various factors that influence travel patterns. The existing models often struggle to capture the dynamics in this field so it's crucial to develop accurate forecasting methods. By leveraging information fusion techniques like smoothing and Autoregressive Integrated Moving Average (ARIMA) our research creates models based on historical data of air passenger volumes. These techniques combine machine learning algorithms and time series analysis to identify dependencies and patterns in the dataset. Through evaluations and comparative analyses, our proposed models demonstrate promising capabilities in forecasting future air passenger volumes. Proof-of-concept experiments based on 5-fold cross-validation demonstrate the efficacy of the proposed approach in capturing underlying trends and seasonality within the dataset.

Cultural foundations of the educational system and legal upbringing in the conditions of contemporary political and legal reality transformation

The article focusses on the special nature of system structural changes occurring in modern Russian society, which directly reflect large-scale changes associated with internal and external aspects of integration of social, political, and legal institutions in the modern political and legal reality of the state, which significantly expands the instrumental sphere in the system of legal regulation, both in the general social context and in the strategic directions of the functioning of the Russian state. The authors have defined educational and legal-educational environment special spheres of modern state-legal space as the object of research because the most important system elements of the modern state function in the conditions of transformational changes in socio-economic, political-legal and socio-cultural plan. The aim of the work is the necessity to actualise a new concept of education in general, and higher education in particular, since in the modern world the institution of higher education is considered to be the most important factor in the development of human resources, in view of the fact that the factor of education in the future will be considered almost the main criterion for sustainable and successful development of any state. The methodological context of this paper is based on a combination of classical general scientific methodology and special techniques and means of scientific knowledge: comparative-legal, historical-legal, and concrete-sociological study of the problems posed in the paper.

Investigations on Microbes Attached to the Cuticle of Phytonematodes.

Nematodes form various associations with soil microbiome. Experimental studies on nematode-attached microbes can improve mechanistic understanding of these associations and lead to new discoveries relevant for the field of nematode biocontrol. Microbial attachment to the surface of phytonematodes is very specific and influenced by a multitude of factors, including the designation of nematodes and microbes, environmental and biological factors in soil, time of incubation, and the ratio and evolutionary trajectories between nematodes and microbes. Here, we describe how the classical nematological and microbiological techniques can be coupled with the advanced molecular tools to study the microbial attachment to phytonematodes in soil. We focus on the characterization of nematode-attached microbes using classical microbiological approaches and high-throughput amplicon sequencing and on the effects of nematode-attached microbes on plant defense responses.

Powdery Scab of Potato: A Diagnostic Guide

Powdery scab, caused by Spongospora subterranea, is a soil- and tuber-borne disease of potato. The fungus-like protozoan pathogen can be found around the world and in almost every large potato-producing state across the United States. Initial signs of infection in the eyes and lenticels of tubers are slightly sunken, purple-brown lesions. When a tuber lesion reaches maturity, the periderm bursts, releasing masses of tiny, powdery balls. The objective of this diagnostic guide is to provide detailed information on the isolation, sampling, pathogenicity testing, and detection of the pathogen in the soil and tubers using classical and molecular techniques to facilitate the identification of the disease in the laboratory and field.