By utilizing the Fourier transform, we present a practical method for evaluating a function of a derivative applied to any other arbitrary function of a single complex variable. As an illustration of this approach, we compute the actions of the displacement and squeeze operators on an arbitrary function, as well as the propagation of paraxial fields, Airy and number states, without the need for algebraic quantum operator techniques or the Fresnel integral.

Recognition, decoding and tracking of vortex patterns is of increasing importance in many fields reaching from astronomical observation of distant galaxies to turbulence phenomena in liquids or gases. Currently, coherent light beams with orbital angular momentum (OAM) are of particular interest for optical communication, metrology, micro-machining or particle manipulation. One common task is to identify characteristic spiral patterns in pixelated intensity maps at real-world signal-to-noise ratios. Recently, Fast Fourier Transform (FFT) was applied to the quantitative analysis of spiral interference patterns of OAM beams. Our study considers this approach in more detail. It is demonstrated that specific information can be extracted by combining conformal mapping by polar transform with determining one- or two-dimensional angular frequency spectra either in spatially fixed or scanning mode. Results of proof-of-principle experiments are presented.

In this work, an operator superquadratic function (in operator sense) for positive Hilbert space operators is defined. Several examples with some important properties together with some observations which are related to the operator convexity are pointed out. Equivalent statements of a non-commutative version of Jensen's inequality for operator superquadratic function are established. A generalization of the main result to any positive unital linear map is also provided.

To make wind power more competitive, it is necessary to reduce turbine downtime and reduce costs associated with wind turbine Operation and Maintenance (O&M). Incorporating machine learning in developing condition-based predictive maintenance methodologies for wind turbines can enhance their efficiency and reliability. This paper presents a monitoring method that utilizes Base Density for the Support Vector Machine (BDSVM) and the evolutionary Fourier spectra of vibrations. This method allows smart monitoring of the function evolution of the turbine. A complex optimal function (FO) for 5-degree order has been developed that will be the boundary function of the BDSVM to timely determine the magnitude, frequency, and place of the failure occurring in wind turbine drive.

The intense motion of a ship can greatly impacts the comfort of crew members and the safety of the vessel. Therefore, accurately estimating and predicting ship attitudes has become an important issue. This paper introduces the latest development in functional deep learning model called DeepOnet. It takes wave height as input and ship motion as output, using a cause-to-result prediction approach. The modeling data used in this study is sourced from publicly available experimental data from the Iowa Institute of Hydraulic Research. Firstly, parameters system tuning was conducted for the neural network's hyperparameters to determine the appropriate combination of parameters. Secondly, the DeepOnet model for wave height and multi-degree-of-freedom motion was established, and the influence of increasing time steps on prediction accuracy was examined. Finally, a comparison was made between the DeepOnet model and the classical time series model LSTM. It was found that the DeepOnet model had a 10-fold improvement in accuracy for roll and heave attitudes. Moreover, as the forecast duration increased, the advantage of DeepOnet showed a trend of strengthening. As a functional prediction model, DeepOnet provides a new promising tool for very short-term prediction of ship motion.

The informational synthesis of neural structures, processes, parameters and characteristics that allow a unified description and modeling as neural machines of natural and artificial neural systems is presented. The general informational parameters as the global quantitative measure of the neural systems computing potential as absolute and relative neural power were proposed. Neural information organizing and processing follows the way in which nature manages neural information by developing functions, functionalities and circuits related to different internal or peripheral components and also to the whole system through a non-deterministic memorization, fragmentation and aggregation of afferent and efferent information, deep neural information processing representing multiple alternations of fragmentation and aggregation stages. The relevant neural characteristics were integrated into a neural machine type model that incorporates unitary also peripheral or interface components as the central ones. The proposed approach allows overcoming the technical constraints in artificial computational implementations of neural information processes and also provides a more relevant description of natural ones.

ABSTRACT Purpose: Tongue image analysis for disease diagnosis is an ancient traditional non-invasive diagnosis technique widely used by traditional medicine practitioners. Deep Learning based multi-label disease detection models offer tremendous potential to clinical decision support systems, by facilitating preliminary diagnosis. Methods: In this work, we propose a multi-label disease detection pipeline, where in observation and analysis of tongue images captured and received via smartphones assist in predicting the health status of an individual. All images are voluntarily given by subjects consulting collaborating physicians. Images thus acquired are first and foremost classified either into a diseased or a normal category by a 5-fold cross-validation algorithm using a convolution neural network (MobileNetV2) model for binary classification. Once the diseased label is predicted, the image is used to diagnose multiple diseases using the prediction algorithm based on DenseNet121. Results: Average accuracy of 93 % was achieved in classifying diseased from normal healthy tongue by detection model with MobileNetV2 architecture. Multilabel disease classification produced more than 90% accurate results for the seven class labels considered. Conclusion: AI based image analysis shows promising results and an extensive dataset could provide further improvements to this approach. Rather than employing high-cost sophisticated image capturing setup, experimenting with smartphone images opens opportunity to provide preliminary health status to individuals on smartphone prior to further line of treatment and diagnosis.

This algorithm is designed to perform Discrete Fourier Transforms (DFT) to convert temporal data into spectral data. This algorithm obtains the Fourier Transforms by studying the Coefficient of Determination of a series of artificial sinusoidal functions with the temporal data, and normalizing the variance data into a high-resolution spectral representation of the time-domain data with a finite sampling rate. What is especially beneficial about this DFT algorithm is that it can produce spectral data at any user-defined resolution.

In previous studies we used Laurent Schwartz’ theory of distributions to rigorously introduce discretizations and periodizations on tempered distributions. These results are now used in this study to derive a validity statement for four interlinking formulas. They are variants of Poisson’s Summation Formula and connect four commonly defined Fourier transforms to one another, the integral Fourier transform, the Discrete-Time Fourier Transform (DTFT), the Discrete Fourier Transform (DFT) and the Integral Fourier transform for periodic functions—used to analyze Fourier series. We prove that under certain conditions, these four Fourier transforms become particular cases of the Fourier transform in the tempered distributions sense. We first derive four interlinking formulas from four definitions of the Fourier transform pure symbolically. Then, using our previous results, we specify three conditions for the validity of these formulas in the tempered distributions sense.

We propose a neural-network-based watermarking method that introduces the quantized activation function that approximates the quantization of JPEG compression. Many neural-network-based watermarking methods have been proposed. Conventional methods have acquired robustness against various attacks by introducing an attack simulation layer between the embedding network and the extraction network. The quantization process of JPEG compression was replaced by the noise addition process in the attack layer of the conventional methods. In this paper, we propose a quantized activation function that can simulate the JPEG quantization standard as it is in order to improve the robustness against the JPEG compression. Our quantized activation function consists of several hyperbolic tangent functions and is applied as an activation function for neural networks. Our network was introduced in the attack layer of ReDMark proposed by Ahmadi et al. to compare it with their method. That is, the embedding and extraction networks had the same structure. We compared the usual JPEG compressed images and the images applying the quantized activation function. The results showed that a network with quantized activation functions can approximate JPEG compression with high accuracy. We also compared the bit error rate (BER) of estimated watermarks generated by our network with those generated by ReDMark. We found that our network was able to produce estimated watermarks with lower BERs than those of ReDMark. Therefore, our network outperformed the conventional method with respect to image quality and BER.

In the dynamic and complex environment of industrial control rooms, operators are often inundated with a multitude of tasks and alerts, which can lead to an overwhelming situation known as task overload. This state can precipitate decision fatigue and a heavier reliance on cognitive biases, potentially compromising the decision-making process. To mitigate such risks, the implementation of decision support systems becomes crucial. These systems are designed to assist operators in making swift and well-informed decisions, particularly when they sense their own judgment may be faltering. Our research introduces an AI-based framework that leverages dynamic influence diagrams and reinforcement learning to construct an effective decision support system. The cornerstone of this framework is the creation of a robust, interpretable, and efficient tool that supports control room operators during critical process disturbances. By integrating expert knowledge, the dynamic influence diagram forms a comprehensive model that captures the uncertainties inherent in complex industrial processes. It is adept at anomaly detection and recommending optimal actions. Moreover, this model is enhanced through a strategic partnership with reinforcement learning algorithms, which fine-tune the recommendations to be more context-specific and precise. The ultimate goal of our framework is to provide operators with a live, reliable decision support system that can significantly improve their response during process upsets. This paper outlines the development of our AI framework and its application within a simulated control room environment. Our findings indicate that the use of decision support systems can lead to improved operator performance and reduced cognitive workload. However, it also reveals a trade-off with situation awareness, which tends to diminish as operators may become overly reliant on the system’s guidance. Trust emerges as a critical factor in the adoption and effectiveness of decision support systems. Our research underscores the importance of balancing the benefits of decision support with the need for maintaining operator engagement and comprehension during process operations.

The validity of our universe as a three-dimensional space (3+1 in relativity) is considered a fundamental fact in physics. In this study, we show that our observed world is thus the output of a prior fundamental operator referred to as an organizer. The organizer is an expansion of projecting operators. It is been shown that identical weighted projecting operators, which are associated with identical particles, generate subspaces of entangled states, whereas groups of unequal weighted coefficients are responsible for finite-size subspaces that are associated with unidentical particles. Considering 3D-subspaces as evidence of the coefficients’ arrangement in our universe, we implement our formalism to describe the implacable vectors, location, momentum, and force within each 3D subspace. By implementing the Heisenberg relation, we drive both the classical and quantum expressions for the laws of motion.

We show that if $f$ is a non-negative superquadratic function, then $A\mapsto\mathrm{Tr}f(A)$ is a superquadratic function on the matrix algebra. In particular, \begin{align*} \tr f\left( {\frac{{A + B}}{2}} \right) +\tr f\left(\left| {\frac{{A - B}}{2}}\right|\right) \leq \frac{{\tr {f\left( A \right)} + \tr {f\left( B \right)} }}{2} \end{align*} holds for all positive matrices $A,B$. In addition, we present a Klein's inequality for superquadratic functions as $$ \mathrm{Tr}[f(A)-f(B)-(A-B)f'(B)]\geq \mathrm{Tr}[f(|A-B|)] $$ for all positive matrices $A,B$. It gives in particular improvement of Klein's inequality for non-negative convex function. As a consequence, some variants of the Jensen trace inequality for superquadratic functions have been presented.

In this paper, we propose a new covering-based set in which the lower and the upper approximation operations are defined by neighborhood systems. We discuss this new type of covering-based set systematically in two steps. First, we study the basic properties of this covering-based set, such as the properties of normality, contraction, and monotone. Second, we discuss the relationship between the new type of covering-based set and the other ten sets proposed.

In this paper, we propose a new covering-based set in which the lower and the upper approximation operation are defined by neighborhood systems. We discuss this new type of covering-based set systematically in two steps. First, we study the basic properties of this covering-based set, such as the properties of normality, contraction, and monotone. Second, we discuss the relationship between the new type of covering-based set and the other ten sets proposed.

The main objective of this present paper is to introduce further extension of extended Caputo fractional derivative operator and establish the extension of an extended fractional derivative of some known elementary functions. Also, we investigate the extended fractional derivative of some familiar special functions, the Mellin transforms of newly defined Caputo fractional derivative operator and generating relations for extension of extended hypergeometric functions.

The main objective of this paper is to introduce k-fractional derivative operator by using the definition of k-beta function. We establish some results related to the newly defined fractional operator such as Mellin transform and relations to k-hypergeometric and k-Appell's functions. Also, we investigate the k-fractional derivative of k-Mittag-Leffler and Wright hypergeometric functions.

This paper proposed an optimal tracking control scheme through adaptive dynamic programming(ADP) for a class of partially unknown discrete-time nonlinear systems based on radial basis function neural network(RBF-NN). In order to acquire the unknown system dynamics, we use two RBF-NNs, the one is used to construct the identifier, and the another is used to directly approximate the steady-state control input, where a novel adaptive law is proposed to update neural network weights. While the optimal feedback control and the cost function are derived via feedforward neural networks approximating, it is proposed to regulate the tracking error, the critic network and the actor network are then trained online to obtain the solution of the associated Hamilton–Jacobi–Bellman (HJB) equation being built under the ADP framework. Simulations verify the effectiveness of the optimal tracking control technique using the neural networks.

This work aims to introduce a novel concept: the Riesz-Dunkl fractional derivatives, within the context of Dunkl type operators. A particularly noteworthy revelation is that when a specific parameter $\kappa$ equals zero, the Riesz-Dunkl fractional derivative smoothly reduces to both the well-known Riesz fractional derivative and the fractional second-order derivative. Furthermore, we introduce a new concept: the fractional Sobolev space. This space is defined and characterized using the versatile framework of the Dunkl transform.

We prove that the Legendre coefficients associated with a function f(x) can be represented as the Fourier coefficients of a suitable Abel-type transform of the function itself. Thus, the computation of N Legendre coefficients can be performed efficiently in O(NlogN) operations by means of a single Fast Fourier Transform of the Abel-type transform of f(x). We also show how the symmetries associated with the Abel-type transform can be exploited to further reduce the computational complexity. The dual problem of calculating the sum of Legendre expansions is also considered. We prove that a Legendre series can be written as the Abel transform of a suitable Fourier series. This fact allows us to state an efficient algorithm for the evaluation of Legendre expansions. Finally, numerical tests are presented to exemplify and confirm the theoretical results.

The unified Mittag-Leffler (ML) function is important factor in formulation of compact form of fractional integrals. In this paper estimations of integral operators, with the unified ML function as kernel are given. The Hadamard inequality in the form of fractional integrals is proved by considering refinement of convexities. These estimations provide various inequalities as refinements of recently published results.

Nowadays the dynamism induced by the constant change of strategic decisions on the markets produces an extra difficulty in the management of an organization. The strategic decisions made by managers can become obsolete in a short period of time. One of the major difficulties in managing a commercial organization is to predict, with some precision degree, the impact some strategic decisions have on the financial results. Business Intelligence (BI) is an area widely used to help managers to make strategic decisions. But the methods used, behind the scenes, to achieve the conclusions are kept secret by BI company-based services. Modelling the environment can be a good option to study the impact of an action, provided by a strategic decision, in a real environment. A good model should give an approximate result of an action applied to a previous state of the environment. Artificial Neural Networks (ANNs) are proven to be excellent in modeling environments with some level of data noise. The same strategic action can have different results in different organizations. A tool that allows an evaluation of a strategic action applied to an environment should have a major importance in the management scope. Modeling the environment should save time and money for the organization to improve the performance of the strategic plan. If one evaluates the state of the environment after a strategic action being applied, it can be possible to mitigate the risk of failure of the strategic plan. As we will be able to verify, it is possible to use ANNs to model strategic environments that should allow the prediction of sales and operating results by the used strategies with some precision, although the level of success will be directly related with the user’s necessity.

Amid escalating urbanization, devising rational commercial space layouts is a critical challenge. Leveraging machine learning, this study uses a Back-propagation (BP) neural network to optimize commercial spaces in Weinan City's central urban area. The results indicate an increased number of commercial facilities with a trend of multi-centered agglomeration and outward expansion. Based on these findings, we propose a strategic framework for rational commercial space development emphasizing aggregation centers, development axes, and spatial guidelines. This strategy provides valuable insights for urban planners in small and medium-sized cities in the Yellow River Basin and metropolitan areas, ultimately showcasing the power of machine learning in enhancing urban planning.

Existing one-shot neural architecture search (NAS) methods have to conduct a search over a giant super-net, which leads to the huge computational cost. To reduce such cost, in this paper, we propose a method, called FTSO, to divide the whole architecture search into two sub-steps. Specifically, in the first step, we only search for the topology, and in the second step, we search for the operators. FTSO not only reduces NAS’s search time from days to 0.68 seconds, but also significantly improves the found architecture's accuracy. Our extensive experiments on ImageNet show that within 18 seconds, FTSO can achieve a 76.4% testing accuracy, 1.5% higher than the SOTA, PC-DARTS. In addition, FTSO can reach a 97.77% testing accuracy, 0.27% higher than the SOTA, with nearly 100% (99.8%) search time saved, when searching on CIFAR10.

Tinnitus is a common phantom auditory percept, believed to be related to plastic changes in the brain due to hearing loss. However, tinnitus can also occur in absence of any clinical hearing loss. Then, since there is no hearing loss, the mechanisms that drive plastic changes remain largely enigmatic. Previous studies showed subtle differences in sound-evoked brain activity associated with tinnitus in subjects with tinnitus and otherwise, normal hearing, but the results are not consistent across studies. Here, we aim to investigate those differences using monaural rather than binaural stimuli. Sound-evoked responses were measured using functional magnetic resonance imaging (MRI) in participants with and without tinnitus. All participants had clinically normal audiograms. The stimuli were pure tones with frequencies between 353 and 8000 Hz, presented monaurally. A Principal Component Analysis (PCA) of the response in the auditory cortex revealed no difference in tonotopic organization, which confirmed earlier studies. A GLM analysis showed hyperactivity in the lateral areas of the bilateral auditory cortex. Consistent with the tonotopic map, this hyperactivity mainly occurred in response to low stimulus frequencies. This may be related to hyperacusis, which was associated with tinnitus found in the parahippocampus. This may reflect an interference between tinnitus and spatial orientation.

Amid the swift progression of the global automobile industry, the aspiration for lightweight vehicle design has surfaced as a crucial approach to boost fuel efficiency and curtail environmental impact. The objective of this study revolves around achieving holistic optimization of vehicle structure via detailed scrutiny of vehicle process characteristics, amalgamated with a Back Propagation neural network (BPNN) optimized by a genetic algorithm (GA) and a topology optimization (TO) method.The process initiates with an examination of the vehicle's technical characteristics, succeeded by an optimization protocol that couples GA with BPNN. This exhaustive optimization procedure derives the best-fit values of design parameters and identifies the globally optimal lightweight design approach. Subsequently, a comprehensive structural optimization is actualized by modifying the topological distribution of the structure.A simulation experiment of the conceptual car body beam skeleton is conducted as a conclusive step, and the anti-collision capacity of the car body beam skeleton is assessed by measuring deformation intrusion. The findings reveal that in the vehicle topology optimization, a comparative analysis of pre and post-optimization results indicates an improved topological density across diverse sections. The topological density of the vehicle's frontal structure escalates from 0.75 to 0.8. Following optimization, the stiffness assessment records a marginal increase (within the range of 0.02–0.05), implying that the lightweight design does not compromise the general rigidity of the structure.The optimized body structure manifests superior crashworthiness in the crash test: the deformation intrusion diminishes by 27% in front-end collisions. In side impacts, the deformation and intrusion at critical points are reduced by 13.15% to 10% respectively. The comprehensive method proposed herein proves to be an efficient strategy to actualize the lightweight design of vehicles.

In this study, we consider a Lambert series whose coefficients are the sum of divisors function. Utilizing the Lambert series in the sequel we introduce a normalized linear operator JR_(α,β) (z) by applying the convolution with Rabotnov function. We then, acquire sufficient conditions for JR_(α,β) (z) to be Univalent, Starlike and Convex respectively. In each component of this study, we expand the derived results by applying two Robin's inequalities, one of which is equivalent to the Riemann hypothesis.

The application of artificial intelligence to point-of-care testing (POCT) disease detection has become a hot research field, in which breath detection which detects the patient's exhaled VOCs combined with sensor arrays of Convolutional Neural Network (CNN) algorithms as a new lung cancer detection is attracting more researchers' attention. However, due to low accuracy, high complexity computation and large number of parameters make the CNN algorithms difficult transplant to the embedded system of POCT devices. A lightweight neural network (LTNet) in this work is proposed to deal with this problem, and meanwhile, achieve high-precision classification of acetone and ethanol gases, which are respiratory markers for lung cancer patients. Compared to currently popular lightweight CNN models such as EfficientNet, LTNet has fewer parameters (32K) and its training weight size is only 0.155 MB. LTNet achieved an overall classification accuracy of 99.06% and 99.14% in the own mixed gas dataset and the University of California (UCI) dataset, which are both higher than that of the five existing models’, and it also offers the shortest training (844.38s and 584.67s) and inference time (23s and 14s) in the same validation set. Compared to the existing CNN models, LTNet is more suitable for resource-limited POCT devices.

In the past two decades, metaheuristic optimization algorithms (MOAs) have been increasingly popular, particularly in logistic, science, and engineering problems. The fundamental characteristics of such algorithms are that they are dependent on a parameter or a strategy. Some online and offline strategies are employed in order to obtain optimal configurations of the algorithms. Adaptive operator selection is one of them, and it determines whether or not to update a strategy from the strategy pool during the search process. In the filed of machine learning, Reinforcement Learning (RL) refers to goal-oriented algorithms, which learn from the environment how to achieve a goal. On MOAs, reinforcement learning has been utilised to control the operator selection process. Existing research, however, fails to show that learned information may be transferred from one problem-solving procedure to another. The primary goal of the proposed research is to determine the impact of transfer learning on RL and MOAs. As a test problem, a set union knapsack problem with 30 separate benchmark problem instances is used. The results are statistically compared in depth. The learning process, according to the findings, improved the convergence speed while significantly reducing the CPU time.

There are many criterion to generalize the concept of numerical radius; one of the most recent interesting generalization is what so called the generalized Euclidean operator radius. Simply, it is the numerical radius of multivariable operators. In this work, several new inequalities, refinements and generalizations are established for this kind of numerical radius.

In this paper, we investigate a new subclass of univalent functions defined by a generalized differential operator, and obtain some interesting properties of functions belonging to the class R^m λµ ( α, β, γ, υ ).

Recently, different extensions of the fractional derivative operator are found in many research papers. The main aim of this paper is to establish an extension of the extended Caputo fractional derivative operator. The extension of an extended fractional derivative of some elementary functions derives by considering an extension of beta function which includes the Mittag-Leffler function in the kernel. Further, an extended fractional derivative of some familiar special functions, the Mellin transforms of newly defined Caputo fractional derivative operator and the generating relations for extension of extended hypergeometric functions also presented in this study.

This paper proposes two max-pooling engines, named the RTB-MAXP engine and the CMB-MAXP engine, with a scalable window size parameter for FPGA-based convolutional neural network (CNN) implementation. The max-pooling operation for the CNN can be decomposed into two stages, i.e., a horizontal axis max-pooling operation and a vertical axis max-pooling operation. These two one-dimensional max-pooling operations are performed by tracking the rank of the values within the window in the RTB-MAXP engine and cascading the maximum operations of the values in CMB-MAXP engine. Both the RBM-MAXP engine and the CMB-MAXP engine were implemented using VHSIC Hardware Description Language (VHDL) and verified by simulations. They have been employed for and tested in our CNN accelerator targeting at the CNN model YOLOv4-CSP-S-Leaky for object detection.

Parkinson’s Disease (PD) is a neurodegenerative and progressive disease that impacts the nerve cells in the brain and varies from person to person. The exact cause of PD is still unknown, and the diagnosis of PD does not include a specific objective test with certainty. Although deep learning has made great progress in medical neuroimaging analysis, these methods are very susceptible to biases present in neuroimaging datasets. An innovative decorrelated deep learning technique is introduced to mitigate class bias and scanner bias while simultaneously focusing on finding distinguishing characteristics in resting-state functional MRI (rs-fMRI) data, which assist in recognizing the PD with good accuracy. The decorrelation function reduces the non-linear correlation between features and bias in order to learn bias-invariant features. The Parkinson’s Progression Markers Initiative (PPMI) dataset, referred to as a single scanner imbalanced dataset in this study used to validate our method. The imbalanced dataset problem affects the performance of the deep learning framework by overfitting to the majority class. To resolve this problem, we propose a new Decorrelated Convolutional Neural Networks (DcCNN) framework by applying decorrelation-based optimization to Convolutional Neural Networks(CNN). An analysis of evaluation metrics comparisons shows that integrating the decorrelation function boosts the performance of PD recognition by removing class bias. Specifically, our DcCNN model performs significantly better than existing traditional approaches to tackle the imbalance problem. Finally, the same framework can be extended to create scanner invariant features without significantly impacting the performance of a model. The obtained dataset is a multi-scanner dataset which leads to scanner bias due to the differences in acquisition protocols and scanners. The multi-scanner dataset is a combination of two datasets, namely PPMI and FTLDNI - frontotemporal lobar degeneration neuroimaging initiative (NIFD) dataset. The results of t-distributed stochastic neighbor embedding (t-SNE) and scanner classification accuracy of our proposed Feature Extraction-DcCNN (FE-DcCNN) model validated the effective removal of scanner bias. Our method achieves an average accuracy of 77.80% on a multi-scanner dataset for differentiating PD from healthy control, which is superior to the DcCNN model trained on a single scanner imbalanced dataset.

Despite the increasing popularity of liquid chromatography-mass spectrometry (LC-MS)-based lipidomics, there is a lack of accepted and validated method for lipid extract quality and quantity assessment prior to LC-MS. Fourier-Transform Infrared Spectroscopy (FTIR) has been reported for quantification of pure lipids, however, the sample complexity and purity complex lipid extract quantification in lipidomics experiments could be impact quantification accuracy. Here, we report comprehensive assessment of the sample matrix on the accuracy of lipid quantification using Attenuated Total Reflectance Fourier-Transform Infrared Spectroscopy (ATR-FTIR). Pure lipids are characterized by CH-and C=O-stretching vibrations on FTIR, with quantitative range of 40–3000 ng and a limit of detection of 12 ng. Sample extraction method and local baseline subtraction during FTIR spectral processing significantly impact lipid quantification by CH-stretching. To facilitate sample quality screening, we developed the Lipid Quality (LiQ) score from a spectral library of common contaminants, using a ratio of peak heights between CH-stretching vibrations maxima and the collective vibrations from amide/amine, CH-stretching minima and sugar moieties. We evaluated LiQ score as a rapid sample quality control method by comparing to total LC-MS intensity of targeted lipidomics of 107 human plasma lipid extracts. Exclusion of poor-quality samples based on LiQ score improved the correlation between FTIR and LC-MS quantification. Finally, the uncertainty of absolute quantification by FTIR was estimated using a 795 ng SPLASH LipidoMix standard to be <10%. In summary, this study identified key parameters for accurate FTIR-based quantification of complex lipid mixture, and developed a rapid workflow requiring only 1 µL of MS-ready sample and < 5 minutes for routine lipidomics sample quality and quantity assessment.

Long-term, high-accuracy mapping of built-up land dynamics is essential for understanding urbanization and its consequences for the environment. Despite advances in remote sensing and classification algorithms, built-up land mapping using early satellite imagery (e.g., from the 2000s and earlier) remains prone to uncertainty. We mapped the extent of built-up land in the North China Plain, one of China’s most important agricultural regions, from 1990 to 2019 at three-year intervals. Using dense time-stack Landsat data, we applied discrete Fourier transformation to create temporal predictors and reduce mapping uncertainties for early years. We improved overall accuracy by 8% compared to using spectral and indices predictors alone. We implemented a temporal correction algorithm to remove inconsistent pixel classifications, further improving accuracy to a consistently high level (>94%) across years. A cross-product comparison showed that our study achieved the highest levels of accuracy across years. Total built-up land in the North China Plain increased from 37,941 km² in 1990–1992 to 131,578 km² in 2017–2019. Consistent, high-accuracy built-up land mapping provides a reliable basis for policy planning in one of the most rapidly urbanizing regions of the planet.

In the paper, we develop some numerical schemes including finite difference scheme and finite volume scheme for the fractional Laplacian operator, and apply the resulted numerical schemes to solve some fractional diffusion equations. First, the fractional Laplacian operator can be characterized as the weak singular integral by a integral operator with zero boundary condition. Second, because of the solution of fractional diffusion equation is usually singular near the boundary, we apply finite difference scheme to discrete fractional Laplacian operator and fractional diffusion equation by fractional interpolation function. Moreover, it is find that the differential matrix of the above scheme is symmetric matrix, and strictly row-wise diagonally dominant in special fractional interpolation function. Third, we show finite volume scheme to discrete fractional diffusion equation by fractional interpolation function, and analyze the properties of differential matrix. Finally, the numerical experiments are given, and verify the correctness of theoretical results and the efficiency of the schemes.

The Fourier Continuous Derivative ($D_C$) offers a unique perspective on fractional differentiation grounded in the theory of Fourier series. This approach has the potential to address problems across various disciplines, including physics, engineering, and mathematics. The primary insight underpinning this approach is that a convex function defined on $\mathbb{Z}$ retains its convexity on $\mathbb{R}$. This paper delves into the Fourier Continuous Derivative, compares it with traditional fractional derivatives, and outlines its possible real-world applications, such as modeling viscoelastic materials, solving wave equations, and financial data analysis.

After proposing a natural metric for the space in which particles spin which implements the principle of maximum frequency, E=hf is generalised and its inverse Fourier transform is calculated. As a necessary result, a metric is found for the space in which quantum particles spin, hence the possibility of explanation of correlation of spacelike-separated particles is opened up.

Robotic systems are increasingly being used in healthcare to improve patient care and support healthcare professionals. These robots are especially effective at performing repetitive tasks. In complex cancer cases, robots can enhance surgical precision and efficiency, resulting in reduced pain for patients and a lower risk of complications. Robot-assisted surgery offers high-quality 3D imaging, improved clarity, and increased efficiency. This review paper examines the application of Artificial Intelligence (AI) and robotic systems in the healthcare domain, specifically focusing on the interaction among operators, patients, and robots. The goal is to promote collaboration and improve healthcare provision through human-robot interaction. We considered already published articles by relevance, to identify the primary safety issues that need addressing for the integration of AI and robots in hospitals. Concluding with insights into understanding the focal points of social errors in Human-Robot Interaction (HRI) is crucial for mitigating these errors. While current technologies have reached a certain level of maturity, there are still numerous challenges in utilizing robot-assisted clinical practice, including technological, safety, clinical, financial, insurance, psychological, social, ethical, and legal issues. In addition, there is an urgent issue that needs to be addressed: the alignment of values in artificial intelligence, ensuring that AI systems reflect ethical principles and human values is crucial to avoid negative consequences such as bias, discrimination, and prejudicial decisions. Resolving this complex issue requires collaboration among clinical staff, researchers, programmers, and political decision-makers from various fields.

Advances in technology have introduced remarkable capabilities, particularly in the realm of gathering and accessing vast amounts of data, which has led to the emergence of the "Big Data" era, presenting exciting opportunities to harness the wealth of the generated information. Traffic management centers comprise a stakeholder that can exploit such data towards improving road network operation. This research, explores the utilization of real traffic data, collected by distinct sources on an interurban motorway: static location based aggregate traffic data and probe vehicle data. The first is collected by traffic detectors, while the second involves patrol vehicles’ GNSS data. The traffic quantity analysed is vehicle speed, while specific emphasis has been given on the ap-plication of heatmaps to represent daily traffic patterns and the utilization of k-means clustering. The performed analysis demonstrates the importance of considering spatiotemporal variables as a unified entity when analysing speed in transportation networks. The limitations of using patrol vehicles as estimators of ambient speed, especially in low and heavy traffic conditions, are deline-ated, while the dual purpose of data gathered from these vehicles towards enhancing driving performance and enabling detector maintenance is emphasized. Valuable traffic insights are offered through comprehensive spatiotemporal speed behavior analysis and data combination. The inte-gration of these techniques enhances decision-making for a streamlined and secure transportation system

The main objective of this present paper is to establish the extension of an extended fractional derivative operator by using an extended beta function recently defined by Parmar et al. by considering the Bessel functions in its kernel. Also, we give some results related to the newly defined fractional operator such as Mellin transform and relations to extended hypergeometric and Appell's function via generating functions.

Ocean surface waves have been utilized as fundamental information in various fields of oceanic research. In this paper, we suggest a simulation and modelling technique for generating an ocean surface wave using an inverse Fast Fourier Transform (iFFT), and we subsequently verify the wave’s accuracy. The conventional method, linear superposition, requires recursive calculation because of the double summation and the time variable; to circumvent this issue, the new algorithm is presented. The Joint North Sea Wave Project (JONSWAP) spectrum is utilized for the ocean surface wave simulation example, and the parameters are the significant wave height (HS) and the zero-crossing wave period (TZ). A coordinate transform for the wavenumber domain was used to apply the inverse FFT algorithm. To verify the accuracy of the simulation result, the relative error between the input condition and the analysis result was calculated. The result for TZ is below 4% relative error, and the maximum relative error for HS is 7%. To avoid the Nyquist frequency for wave-field analysis and simulation, the minimum grid size was calculated by twice applying the maximum wavenumber.

The therapeutic, attenuative, and morphological effects of proprietary neural stem cell-derived extracellular vesicles (NSC EVs, AB126) produced by Aruna Bio, Inc. were assessed in a range of in vitro and in vivo models of stroke. We emphasize that modulation of neuroinflammation is a key target and suggest further studies to advance our understanding of the mechanisms of action and ultimately how best to dose and monitor the benefits of AB126 in stroke patients.

The theory of the continuous two-dimensional (2D) Fourier Transform in polar coordinates has been recently developed but no discrete counterpart exists to date. In this paper, we propose and evaluate the theory of the 2D discrete Fourier Transform (DFT) in polar coordinates. This discrete theory is shown to arise from discretization schemes that have been previously employed with the 1D DFT and the discrete Hankel Transform (DHT). The proposed transform possesses orthogonality properties, which leads to invertibility of the transform. In the first part of this two-part paper, the theory of the actual manipulated quantities is shown, including the standard set of shift, modulation, multiplication, and convolution rules. Parseval and modified Parseval relationships are shown, depending on which choice of kernel is used. Similar to its continuous counterpart, the 2D DFT in polar coordinates is shown to consist of a 1D DFT, DHT and 1D inverse DFT.

There are several challenges on how to attain energy efficiency while maintaining balance among factors affecting energy consumption such as power rating and temperature setpoints of cooling units, room temperature and humidity, and indoor air quality (IAQ). A real-time energy and IAQ monitoring system were installed in an educational building to profile the operational power consumption of inverter-based air condition unit (ACU) installed in each room. Polynomial curve and neural fitting regression analysis were applied to the real-time power consumption, indoor temperature and humidity, and carbon dioxide (CO2) level data. The derived models were able to provide the stabilizing indoor thermal and air conditions of the room to reach steady state ACU power consumption. These collected data and calculated parameters can be used to define rules in automating control of cooling appliances for an efficient energy utilization. The regression approaches, using real-time data, have determined the influence of indoor heat conditions and carbon dioxide levels on ACU power consumption. These parameters were utilized to establish consistent values for temperature, humidity, and carbon dioxide levels under stable settings of inverter-based air conditioning units.

Antimony (Sb) has gained significance as a critical raw material (CRM) within the European Union (EU) due to its strategic importance in various industrial sectors, particularly in the textile industry for flame retardants and as a component of Sb-based semiconductor materials. Moreover, Sb is emerging as a potential alternative for anodes used in lithium-ion batteries, a key element in the Energy transition. This study focused on exploring the feasibility of identifying and quantifying Sb mineralizations through the spectral signature of soils using reflectance spectroscopy, a non-invasive remote sensing technique, and by employing deep learning algorithms such as Convolutional Neural Networks (CNNs). Common signal preprocessing techniques were applied to the spectral data, and the soils were analyzed by Inductively Coupled Plasma Mass Spectrometry (ICP-MS). Despite achieving high R-squared values, the study faces a significant challenge of generalization of the model to new data. Despite the limitations, this study provides valuable insights into potential strategies for future research in this field.

This study explores the properties and behavior of bi-close-to-convex functions, introducing new subclasses defined by their relationship with fractional differential operator and bi-univalent functions. Using the Faber polynomial technique, we derive upper bounds for the n^{th} coefficient of functions in these classes. We also investigate the erratic behavior of initial coefficients in bi-close-to-convex functions, as characterized by the (λ,q)-fractional differintegral operator. Furthermore, we address Fekete-Szegö problems and present notable findings from our investigation, contributing to the continued growth and refinement of geometric function theory, yielding new insights and practical uses.

The Bessel function of the first kind J_N(kx) is expanded in a Fourier-Legendre series, as is the modified Bessel functions of the first kind I_N(kx) . Known polynomial approximations for the range −3≤x≤3 (having five-digit accuracy) are compared with those arising from this Legendre series and substitute versions are given with twice the number of terms and range (with five-digit accuracy or having fifteen-digit accuracy over −3≤x≤3). It is shown that infinite series of like-powered contributors (involving _2F_3 hypergeometric functions) extracted from the Fourier-Legendre series may be summed, having values that are inverse powers of the first five primes 1/(2^i 3^j 5^k 7^l 11^mm) for powers of order x24.

We study the application of Optimal Control Theory to Ion Cyclotron Resonance. We test the validity and the efficiency of this approach for the robust excitation of an ensemble of ions with a wide range of cyclotron frequencies. Optimal analytical solutions are derived in the case without any pulse constraint. A gradient-based numerical optimization algorithm is proposed to take into account limitation in the control intensity. The efficiency of optimal pulses is investigated as a function of control time, maximum amplitude and range of excited frequencies. A comparison with adiabatic and SWIFT pulses is done. On the basis of recent results in Nuclear Magnetic Resonance, this study highlights the potential usefulness of optimal control in Ion Cyclotron Resonance.

In this paper, the Fourier-based synchrosqueezing transform (FSST) method is introduced into the power system to realize low frequency oscillation identification. Firstly, the modal components of low frequency oscillation signal are separated by FSST, and calculating the instantaneous parameters including magnitude, frequency and phase of every mode component with Hilbert transform. Then , calculating the damping ration of every modal component based on above parameters and derived the formulas. Thus, it realized effective identification of of modal parameters of low frequency oscillation signal. The experimental results of simulated data and 16-generator system demonstrate the validity and correctness of the FSST method. Comparing with the classical Prony method shows that the FSST method is better in the identification accuracy when the low frequency oscillation signal is polluted by noise. Finally, the effectiveness of the FSST in Actual power grid is verified based on the real data from Sichuan power grid.

The theory of fractional calculus extends the order of classical integer calculus from integer to non-integer. As a new engineering application tool, it has made many important research achievements in many fields, including image processing. This paper mainly studies the application of fractional calculus theory in image enhancement and denoising, including the basic theory of fractional calculus and its amplitude frequency characteristics, the application of fractional differential operator in image enhancement, and the application of fractional integral operator in image denoising. The experimental results show that the fractional calculus theory has more special advantages in image enhancement and denoising. Compared with the existing integer order image enhancement operators, the fractional differential operator can more effectively enhance the "weak edge" and "strong texture" details of the image. The fractional order integral image denoising operator can not only improve the signal-to-noise ratio of the image compared to traditional denoising methods, but also better preserve detailed information such as edges and textures of the image.

In this paper, we introduce two subclasses of analytic and Spirallike functions and investigate convolution properties, the necessary and sufficient condition, coefficient estimates and inclusion properties for these classes .

Any quantization maps linearly functions on a phase space to symmetric operators in a Hilbert space. Covariant integral quantization combines operator-valued measure with symmetry group of the phase space. Covariant means that the quantization map intertwines classical (geometric operation) and quantum (unitary transformations) symmetries. Integral means that we use all ressources of integral calculus, in order to implement the method when we apply it to singular functions, or distributions, for which the integral calculus is an essential ingredient. In this paper we emphasize the deep connection between Fourier transform and covariant integral quantization when the Weyl-Heisenberg and affine groups are involved. We show with our generalisations of the Wigner-Weyl transform that many properties of the Weyl integral quantization, commonly viewed as optimal, are actually shared by a large family of integral quantizations.

Microgrids of varying size and applications are regarded as a key feature of modernizing the power system. The protection of those systems, however, has become a major challenge and a popular research topic for the reason that it involves greater complexity than traditional distribution systems. This paper addresses the issue through a novel approach which utilizes detailed analysis of current and voltage waveforms through windowed fast Fourier and wavelet transforms. The fault detection scheme involves bagged decision trees which use input features extracted from the signal processing stage and selected by correlation analysis. The technique was tested on a microgrid model developed using PSCAD/EMTDS, which is inspired from an operational microgrid in Goldwind Sc. Tech. Co. Ltd, in Beijing, China. The results showed great level of effectiveness to accurately identify faults from other non-fault disturbances, precisely locate the fault and trigger opening of the right circuit breaker/s under different operation modes, fault resistances and other system disturbances.

In this paper, a multi-operator differential evolution algorithm (MODE) is proposed to solve the Optimal Power Flow (OPF) problem and is called MODE-OPF. The MODE-OPF utilizes the strengths of more than one differential evolution (DE) operator in a single algorithmic framework. Additionally, an adaptive method (AM) is proposed to update the number of solutions evolved by each DE operator based on both the diversity of population and quality of solutions. This adaptive method has the ability to maintain diversity at the early stages of the optimization process and boost convergence at the later ones. The performance of the proposed MODE-OPF is tested by solving OPF problems for both small and large IEEE bus systems (i.e., IEEE-30 and IEEE-118) while considering the intermittent solar and wind power generation. To prove the suitability of this proposed algorithm, its performance has been compared against several state-of-the-art optimization algorithms, where MODE-OPF outperforms other algorithms in all experimental results and thereby improving a network's performance with lower cost. MODE-OPF decreases the total generation cost up to 24.08%, the real power loss up to 6.80% and the total generation cost with emission up to 8.56%.

Accurate classification of objects in 3D point clouds is a significant problem in several applications, such as autonomous navigation and augmented/virtual reality scenarios, which has become a research hot spot. In this paper, we presented a deep learning strategy for 3D object classification in augmented reality. The proposed approach is a combination of the GRU and LSTM. LSTM networks learn longer dependencies well, but due to the number of gates, it takes longer to train; on the other hand, GRU networks have a weaker performance than LSTM, but their training speed is much higher than GRU, which is The speed is due to its fewer gates. The proposed approach used the combination of speed and accuracy of these two networks. The proposed approach achieved an accuracy of 0.99 in the 4,499,0641 points dataset, which includes eight classes (unlabeled, man-made terrain, natural terrain, high vegetation, low vegetation, buildings, hardscape, scanning artifacts, cars). Meanwhile, the traditional machine learning approaches could achieve a maximum accuracy of 0.9489 in the best case.

This paper presents Chebyshev Type inequalities for the Riemann-Liouville variable-order fractional integral operator using two synchronous functions on the set of real numbers. It is the first result of its kind in the current literature using variable-order Riemann-Liouville fractional integral operator. Some special cases for the result obtained in the paper are discussed.

We consider rotational hypersurface in the four dimensional Euclidean space. We calculate the mean curvature and the Gaussian curvature, and some relations of the rotational hypersurface. Moreover, we define the third Laplace-Beltrami operator and apply it to the rotational hypersurface.

Intuitionistic fuzzy set, which can be represented using the triangular intuitionistic fuzzy number (TIFN), is a more generalized platform for expressing imprecise, incomplete and inconsistent information when solving multi-criteria decision-making problems, as well as for reflecting the evaluation information exactly in different dimensions. In this paper, the TIFN has been applied for solving some multi-criteria decision-making problems by developing a new triangular intuitionistic fuzzy geometric aggregation operator, that is the generalized triangular intuitionistic fuzzy ordered weighted geometric averaging (GTIFOWGA) operator, and defining some triangular intuitionistic fuzzy geometric aggregation operators including the triangular intuitionistic fuzzy weighted geometric averaging (TIFWGA) operator, the ordered weighted geometric averaging (TIFOWGA) operator and the hybrid geometric averaging (TIFHWGA) operator. Based on these operators, a new approach for solving multicriteria decision-making problems when the weight information is fixed has been proposed. Finally, the proposed method has been compared with some similar existing computational approaches by virtue of a numerical example to verify its feasibility and rationality.

Functional connectivity (FC) is a potential candidate that can increase the performance of brain-computer interfaces (BCIs) in the elderly because of its compensatory role in neural circuits. However, it is difficult to decode FC by current machine learning techniques because of a lack of its physiological understanding. To investigate the suitability of FC in BCI for the elderly, we propose the decoding of lower- and higher-order FCs using a convolutional neural network (CNN) in six cognitive-motor tasks. The layer-wise relevance propagation (LRP) method describes how age-related changes in FCs impact BCI applications for the elderly compared to younger adults. Seventeen younger (24.5±2.7 years) and twelve older (72.5±3.2 years) adults were recruited to perform tasks related to hand-force control with or without mental calculation. CNN yielded a six-class classification accuracy of 75.3% in the elderly, exceeding the 70.7% accuracy for the younger adults. In the elderly, the proposed method increases the classification accuracy by 88.3% compared to the filter-bank common spatial pattern (FBCSP). LRP results revealed that both lower- and higher-order FCs were dominantly overactivated in the prefrontal lobe depending on task type. These findings suggest a promising application of multi-order FC with deep learning on BCI systems for the elderly.

Deep Learning (DL) oriented document processing is widely used in different fields for extraction, recognition, and classification processes from raw corpora of data. The article examines the application of deep learning approaches, based on different neural network methods, including Gated Recurrent Unit (GRU), Long Short-Term Memory (LSTM), and Convolutional Neural Networks (CNN). The compared models were combined with two different word embedding techniques, namely: Bidirectional Encoder Representations from Transformers BERT and Gensim Word2Vec. The models are designed to evaluate the performance of architectures based on neural network techniques for the classification of CVs of Moroccan engineering students at ENSAK(National School of Applied Sciences of Kenitra, Ibn Tofail University). The used dataset included resumes collected from engineering students at ENSAK in 2023 for a project on the employability of Moroccan engineers in which new approaches were applied, especially machine learning, deep learning, and big data. Accordingly, 867 resumes were collected from five specialties of study (Electrical Engineering, Networks and Systems Telecommunications, Computer Engineering, Automotive Mechatronics Engineering, Industrial Engineering). The results revealed good performance of the proposed models based on the BERT embedding approach compared to models based on the Gensim Word2Vec embedding approach. Accordingly, the CNN-GRU/Bert model achieved slightly better accuracy with 0.9251 compared to other hybrid models.

Optical artificial neural networks (ONNs) — analog computing hardware tailored for machine learning [1,2] — have significant potential for ultra-high computing speed and energy efficiency [3]. We propose a new approach to architectures for ONNs based on integrated Kerr micro-comb sources [4] that is programmable, highly scalable and capable of reaching ultra-high speeds. We experimentally demonstrate the building block of the ONN — a single neuron perceptron — by mapping synapses onto 49 wavelengths of a micro-comb to achieve a high single-unit throughput of 11.9 Giga-FLOPS at 8 bits per FLOP, corresponding to 95.2 Gbps. We test the perceptron on simple standard benchmark datasets — handwritten-digit recognition and cancer-cell detection — achieving over 90% and 85% accuracy, respectively. This performance is a direct result of the record small wavelength spacing (49GHz) for a coherent integrated microcomb source, which results in an unprecedented number of wavelengths for neuromorphic optics. Finally, we propose an approach to scaling the perceptron to a deep learning network using the same single micro-comb device and standard off-the-shelf telecommunications technology, for high-throughput operation involving full matrix multiplication for applications such as real-time massive data processing for unmanned vehicle and aircraft tracking.

Fokker-Planck PDEs (incl. diffusions) for stable Lévy processes (incl. Wiener processes) on the joint space of positions and orientations play a major role in mechanics, robotics, image analysis, directional statistics and probability theory. Exact analytic designs and solutions are known in the 2D case, where they have been obtained using Fourier transform on $SE(2)$. Here we extend these approaches to 3D using Fourier transform on the Lie group $SE(3)$ of rigid body motions. More precisely, we define the homogeneous space of 3D positions and orientations $\mathbb{R}^{3}\rtimes S^{2}:=SE(3)/(\{\mathbf{0}\} \times SO(2))$ as the quotient in $SE(3)$. In our construction, two group elements are equivalent if they are equal up to a rotation around the reference axis. On this quotient we design a specific Fourier transform. We apply this Fourier transform to derive new exact solutions to Fokker-Planck PDEs of $\alpha$-stable Lévy processes on $\mathbb{R}^{3}\rtimes S^{2}$. This reduces classical analysis computations and provides an explicit algebraic spectral decomposition of the solutions. We compare the exact probability kernel for $\alpha = 1$ (the diffusion kernel) to the kernel for $\alpha=\frac12$ (the Poisson kernel). We set up SDEs for the Lévy processes on the quotient and derive corresponding Monte-Carlo methods. We verify that the exact probability kernels arise as the limit of the Monte-Carlo approximations.

This paper presents an approach to the analysis of beams with rectangular cross-sections subjected to Saint-Venant torsion using the Fourier analysis, body forces being not considered. The Saint-Venant torsion of beams, also called free torsion or unrestrained torsion, is characterized by the absence of axial stresses due to torsion; only shear stresses are developed. The solution to this torsion problem consists of finding the Prandtl stress function that satisfies the governing equation and the boundary conditions, the governing equation being such that the Laplacian of the stress function has a constant value within the cross-section. In this paper, Fourier sine series was utilized to describe the constant value of the above mentioned Laplacian, while double sine series or simple sine series was utilized to describe the Prandtl stress function. Closed-form solutions in form of infinite series were derived for shear stresses, torsional constant and warping function. Those solutions were identical to the exact solutions.

This scientific paper presents a comprehensive investigation into transient Fourier analysis in some electrical engineering applications. The article deals with two effective approaches for solving transient analysis whose application is rather novel. The first contribution uses combined the Fourier series analytic Laplace-Carson (L­C) transform methods in the complex domain using complex time vectors, thereby significantly simplifying the calculation of the original function. As the inverse transform goes back into the time domain, it employs the Cauchy-Heaviside (C­H) method. The second contribution uses the Fourier transform (F­Τ)for transient analysis of a power converter electrical circuit with the passive and the active load. The method of complex conjugated amplitudes is used for steady-state analysis. Both contributions represent a new approach to this paper. The starting point is the Fourier series/expansions, computation of the Fourier coefficients, then continuing by solving the steady and transient states of the system and confirming the transient states using the Fourier transform. To validate our findings, the worked-out analytical results are verified by modelling in Matlab/Simulink environment.

Bacterial infections and resistance to antibiotic drugs represent the highest challenges to public health. The search for new and promising compounds with anti-bacterial activity is a very urgent matter. In order to promote the development of platforms enabling to the discovery of compounds with anti-bacterial activity, Fourier Transformed Mid-Infrared (FT-MIR) spectroscopy associated with the machine learning algorithms were used to predict the impact of compounds extracted from Cynara cardunculus against Escherichia coli cells. According to the plant tissue (seeds, dry and fresh leaves, and flowers) and the solvents (ethanol, methanol, acetone, ethyl acetate, and water), compounds with different compositions concerning, phenol content, antioxidant, and antimicrobial activity were obtained. Principal component analysis of spectra, allowed to discriminate compounds that inhibit the E. coli growth, according to the conventional assay. The supervised classification models enabled the prediction of the compound's impact on the E. coli growth, with the accuracy for the test data: Partial least squares-discriminant analysis of 94%; Support vector machines of 89%; k-Nearest neighbor of 72%; and a Backpropagation network of 100%. According to the promising results, the integration of FT-MIR spectroscopy with machine learning presents a high potential to promote the discovery of new compounds with antibacterial activity, thereby streamlining the drug exploratory process.

Evaluation of biliary strictures remains a challenge due to the low sensitivity of standard diagnostic work up, but the introduction of direct single-operator cholangioscopy (DSOC) changed this paradigm. Aim of our study was to evaluate diagnostic performance of DSOC and DSOC-targeted biopsies, intraductal ultrasound (IDUS) and brush cytology in patients with indeterminate biliary stricture (IBS). We evaluated patients who underwent advanced diagnostic work up for IBS in our endoscopy unit from ‘01/2018 to ‘12/2022; all patients had at least one previous attempt to characterize the biliary stricture. Final diagnosis was based on surgical pathology and/or clinical and radiological follow-up of at least 12 months. A total of 57 patients with a mean age of 67.2 ± 10.0 years were included, with a mean follow up of 18.2 ± 18.1 months. IBS were mostly located in the distal common bile duct (45.6%) and final diagnosis was consistent with malignancy in 35 patients (61.4%). DSOC and IDUS showed a significantly higher accuracy (89.5% and 82.7% respectively) compared to standard cytology (61.5%, p <0.05). In our experience, DSOC visualization and IDUS both demonstrated an optimal diagnostic yield in the differentiation of IBS, with an acceptable safety profile both quantitatively and qualitatively.

The multivariate Gaussian random fields with matrix-based scaling laws are widely used for inference in statistics and many applied areas. In such contexts interests are often in symmetry and in the rates of change of spatial surfaces in any given direction. This article analyzes the almost sure sample function behavior for operator fractional Brownian motion, including multivariate fractional Brownian motion. We obtain the estimations of small ball probability and the strongly locally nondeterministic for operator fractional Brownian motion in any given direction. Applying these estimates we obtain Chung's laws of the iterated logarithm for spatial surfaces of operator fractional Brownian motion. Our results show that the precise rates of change of spatial surfaces are completely determined by the self-similarity exponent.

Fractional differential mathematical model unfolding the dynamics of the COVID-19 pandemic in India is presented and explored in this paper. The purpose of this study is to estimate the future outbreak of disease and potential control strategies using mathematical models in India as a whole country as well as in some of the states of the country. This model is calibrated based on reported cases of infections over the month of April 2020 in India. We have used iterative fractional complex transform method to find approximate solutions of the model having modified Riemann Liouville fractional differential operator. We have also carried out a comparative analysis between actual and estimated cumulative cases graphically, moreover, most sensitive parameters for basic reproduction number$(R_0)$ are computed and their effect on transmission dynamics of COVID-19 pandemic is investigated in detail.

In the present research, we will develop some integral inequalities of Hermite Hadamard type for differentiable η-convex function. Moreover, our results include several new and known results as special cases.

In this paper, the transmutation operator method is used to construct an exact solution to the initial boundary value problem for the equation of multidimensional free transverse vibration of a thin elastic plate with a singular Bessel operator acting on geometric variables. We emphasize that multidimensional Erdélyi–Kober operators of fractional order have the property of a transmutation operator, allowing one to transform more complex multidimensional partial differential equations with singular coefficients acting over all variables into simpler ones. If formulas for solutions are known for a simple equation, then we also obtain representations for solutions to the first complex partial differential equation with singular coefficients. In particular, it is successfully applied to the singular differential equations, especially with Bessel-type operators. Using this operator, the considered problem is reduced to a similar problem without the Bessel operator. Based on the solution to the auxiliary problem, an exact solution to the original problem is constructed and analyzed.

The special affine Fourier transform (SAFT) is a useful and powerful analyzing tool in signal processing, optics and communications. In this paper, we mainly discuss the randomized nonuniform sampling and reconstruction for random signals bandlimited in the SAFT domain. First, we show that the nonuniform sampling is identical to the uniform sampling after a pre-filter in the sense of second order statistic characters. Then, we propose an approximate reconstruction based on sinc interpolation for the nonuniform sampling of random signals bandlimited in the SAFT domain. Finally, we give the mean square error estimate for the proposed approximate recovery approach.

Exposure to quasi-electrostatic field induced currents is a hazard of live-line transmission work. These steady-state induced currents are typically less than 1 mA, and their sensory effects range from imperceptible to painful depending on the person and conditions such as contact area and duration. Permanent injury from these currents is unlikely but they can distract workers, increasing the risk of injury from falls or other dangers. Identifying contact current severity and training workers can help reduce risk of accidents. Measuring induced currents along a climbing route is time consuming and simulation is challenging because of geometric complexity of the worker, transmission structure, conductor bundles, and electric fields in the climbing space. This research explores calculation of worker contact current using a recently developed adaptation of the charge simulation method. The method uses Fourier principles to improve computational efficiency when explicitly modeling all bundle subconductors. The research also examines reasonable simplifications for modeling lattice structures and human geometry. Calculated results compare well to measured currents for a worker climbing a 400 kV lattice structure. This indicates the method is a practical option for calculating the severity of steady-state contact currents. A simple calculation is suggested for estimating these currents.

Texture is essential information for image representation, capturing patterns, and structures. Consequently, texture plays a crucial role in the manufacturing industry and has been extensively studied in the fields of computer vision and pattern recognition. However, real-world textures are susceptible to defects, which can degrade the image quality and cause various issues. Therefore, there is a need for accurate and effective methods to detect texture defects. In this study, a simple autoencoder and Fourier transform were employed for texture defect detection. The proposed method combines Fourier transform analysis with the reconstructed template obtained from the simple autoencoder. Fourier transform is a powerful tool for analyzing the frequency domain of images and signals. Moreover, analyzing the frequency domain enables effective defect detection because texture defects often exhibit characteristic changes in specific frequency ranges. The proposed method demonstrates effectiveness and accuracy in detecting texture defects. Experimental results are presented to evaluate its performance and compare it with those of existing approaches.

ABC-OCT, Affordable B-scan Camera-based Optical Coherence Tomography, implements Fourier-Domain Optical Coherence Tomography with real-time display using cross-platform C++ and the OpenCV framework. The software can be compiled using current versions of GCC for *nix/Mac and Microsoft^® Visual Studio for Windows. Full functionality of ABC-OCT needs the camera SDK from QHYCCD and a QHYCCD camera to be connected; but the code can be easily modified to support other camera drivers, as is shown by an included demo version which can use any installed webcam. The code is made available under the MIT license. The software is available from GitHub (https://github.com/hn-88/FDOCT).

This study addresses the critical challenge of Speech Enhancement (SE) in noisy environments, where the deployment of Deep Neural Networksolutions on microcontrollers is hindered by their extensive computational demands. Focusing on this gap, our research introduces a novel SE method optimized for MCUs, employing a 2-layer GRU model that capitalizes on perceptual speech properties and innovative training methodologies. By incorporating self-reference signals and a dual strategy of compression and recovery based on the Mel scale, we develop an efficient model tailored for low-latency applications. Our GRU-2L-128 model demonstrates a significant reduction in size and computational requirements, achieving a 14.2× decrease in model size and a 409.1× reduction in operations compared to traditional DNN methods like DCCRN, without compromising performance. This advancement offers a promising solution for enhancing speech intelligibility in resource-constrained devices, marking a pivotal step in SE research and application.

The purpose of this paper is to summarize and share the field experiment results of KEPCO's project consortium to create a TSO-DSO-DERA interaction scheme. The field experiment was conducted based on the prequalification algorithm proposed in the previous research from the same consortium and was designed to verify the validity of the algorithm under realistic grid conditions. In addition, during the course of the field experiment, it was found that points that were missed or not given much importance in the existing prequalification algorithm could affect the completeness of the overall system, and then practical improvements were made to improve it. The demonstration results confirm that the proposed algorithm is effective in real-world grid environments and can help DSOs ensure the reliability of the distribution system while supporting DERA's participation in the wholesale market using the proposed prequalification scheme.

The ability to handle spatiotemporal information makes contribution for improving the prediction performance of machine RUL. However, most existing models for spatiotemporal information processing are not only complex in structure but also lack adaptive feature extraction capabilities. Therefore, a lightweight operator with adaptive spatiotemporal information extraction ability named Involution GRU (Inv-GRU) is proposed for aero-engine RUL prediction. Involution, the adaptive feature extraction operator, is replaced by the information connection in the gated recurrent unit for obtaining the adaptively spatiotemporal information extraction ability and reducing the parameters. Thus, Inv-GRU can well extract the degradation information the of aero-engine. Then for RUL prediction task, the Inv-GRU based deep learning (DL) framework is firstly constructed, where features extracted by Inv-GRU and several human-made features are separately processed to generate the health indicators (HIs) from multi-raw data of aero-engines. Finally, fully connection layers are adopted are adopted to reduce dimension and regress RUL based on the generated HIs. By applying the Inv-GRU based DL framework to the Commercial Modular Aero Propulsion System Simulation (C-MAPSS) datasets, successful predictions of aero-engines RUL have been achieved. Comparative analysis reveals that the proposed model exhibits superior overall prediction performance compared to recent public methods.

The methods for constructing solutions to integro-differential equations of the Volterra type are considered. The equations are related to fractional conformable derivatives. Explicit solutions of homogeneous and inhomogeneous equations are constructed and a Cauchy-type problem is studied. It should be noted that the considered method is based on the construction of normalized systems of functions with respect to a differential operator of fractional order.

The theory of the continuous two-dimensional (2D) Fourier Transform in polar coordinates has been recently developed but no discrete counterpart exists to date. In the first part of this two-paper series, we proposed and evaluated the theory of the 2D discrete Fourier Transform (DFT) in polar coordinates. The theory of the actual manipulated quantities was shown, including the standard set of shift, modulation, multiplication, and convolution rules. In this second part of the series, we address the computational aspects of the 2D DFT in polar coordinates. Specifically, we demonstrate how the decomposition of the 2D DFT as a DFT, Discrete Hankel Transform (DHT) and inverse DFT sequence can be exploited for efficient code. We also demonstrate how the proposed 2D DFT can be used to approximate the continuous forward and inverse Fourier transform in polar coordinates in the same manner that the 1D DFT can be used to approximate its continuous counterpart.

Characterization of cancer cells and neural stem cells indicates that tumorigenicity and pluripotency are coupled cell properties determined by neural stemness, and tumorigenesis represents a process of progressive loss of original cell identity and gain of neural stemness. This reminds of a most fundamental process required for the development of the nervous system and body axis during embryogenesis, i.e., embryonic neural induction. Neural induction is that, in response to extracellular signals that are secreted by the Spemann-Mangold organizer in amphibians or the node in mammals and inhibit epidermal fate in ectoderm, the ectodermal cells lose their epidermal fate and assume the neural default fate and consequently, turn into neuroectodermal cells. They further differentiate into the nervous system and also some non-neural cells via interaction with adjacent tissues. Failure in neural induction leads to failure of embryogenesis, and ectopic neural induction due to ectopic organizer or node activity or activation of embryonic neural genes causes a formation of secondary body axis or a conjoined twin. During tumorigenesis, cells progressively lose their original cell identity and gain of neural stemness, and consequently, gain of tumorigenicity and pluripotency, due to various intra-/extracellular insults in cells of a postnatal animal. Tumorigenic cells can be induced to differentiation into normal cells and integrate into normal embryonic development within an embryo. However, they form tumors and cannot integrate into animal tissues/organs in a postnatal animal because of lack of embryonic inducing signals. Combination of studies of developmental and cancer biology indicates that neural induction drives embryogenesis in gastrulating embryos but a similar process drives tumorigenesis in a postnatal animal. Tumorigenicity is the manifestation of aberrant occurrence of pluripotent state in a postnatal animal. Pluripotency and tumorigenicity are both but different manifestations of neural stemness in pre- and postnatal stage, respectively, of animal life. The unique property of neural stemness is derived from the evolutionary advantage of neural genes and the neural-biased state of the last common unicellular ancestors of metazoan. Based on these findings, I discuss about some confusion in cancer research, propose to distinguish the causality and associations and discriminate causal and supporting factors involved in tumorigenesis, and suggest revisiting the focus of cancer research.

The main purpose of this article is to identify brain diseases such as Alzheimer's and Parkinson's in an intelligent way using Python software and processing the function of neurons in the neural network areas of the brain, which are classified into different components, and the data is based on the information obtained from FMRI images using algorithms artificial intelligence can intelligently diagnose the type of disease. Therefore, by using spatial clustering based on the deep learning method with noise algorithm (DBSCAN), fMRI brain image and fMRI brain surface complexity are classified, and then image preprocessing will be applied to fMRI images by using artificial intelligence neural networks (ANN) algorithm. became. Then, by using the ANN algorithm and Deep CNN topology of the brain neural network, the type of disease in the brain can be diagnosed by simulating the performance of an artificial neural network (ANN) in Python software. Deep machine learning-based methods, especially algorithms based on neural networks, have shown great success in medical image analysis for various tasks including brain tumor detection, segmentation, and classification, and Alzheimer's and epilepsy. In this research, we propose an integrated model based on a convolutional neural network for simultaneous recognition and classification of brain diseases for intelligent diagnosis of tumors and epilepsy. The average accuracy obtained from our proposed model is 97.89 percent accuracy and 91.66 percent specificity.

Covid-19 is a lung disease caused by a Coronavirus family virus. Due to its extraordinary prevalence and death rates, it has spread quickly to every country in the world. Thus, achieving peaks and outlines and curing different types of relapses is extremely important. Given the worldwide prevalence of Coronavirus and the participation of physicians in all countries, Information has been gathered regarding the properties of the virus, its diverse types, and the means of analyzing it. Numerous approaches have been used to identify this evolving virus. It is generally considered the most accurate and acceptable method of examining the patient's lungs and chest through a CT scan. As part of the feature extraction process, a method known as fractional Fourier transform (FrFT) has been applied as one of the time-frequency domain transformations. The proposed method was applied to a database consisting of 2481 CT images. Following the transformation of all images into equal sizes and the removal of non-lung areas, multiple combination windows are used to reduce the number of features extracted from the images. In this paper, the results obtained for KNN and SVM classification have been obtained with accuracy values of 99.84% and 99.90%, respectively.

Incorporating linear-scanning MEMS micromirrors into Fourier transform spectral acquisition systems can greatly reduce the size of the spectrometer equipment, making portable Fourier transform spectrometers (FTS) possible. How to minimize the tilting of the MEMS mirror plate during its large linear scan is a major problem in this application. In this work, an FTS system has been constructed based on a biaxial MEMS micromirror with a large piston displacement of 180 μm, and a biaxial H∞ robust controller is designed. Compared with open-loop control and PID closed-loop control, H∞ robust control has good stability and robustness. The experimental results show that the stable scanning displacement reaches 110.9 μm under the H∞ robust control, and the tilting angle of the MEMS mirror plate in that full scanning range falls within ±0.0014°. Without control, the FTS system cannot generate meaningful spectra. In contrast, the FTS yields a clean spectrum with an FWHM spectral linewidth of 96 cm-1 under the H∞ robust control. Moreover, the FTS system can maintain good stability and robustness under various driving conditions.

The main sources of intrinsic noise in excitable cells at the microcircuit and network levels are the stochastic characteristics of ion channel gating and activation of the synaptic conductance. Studies using in vivo, in vitro, and in silico methods to examine the effects of synaptic background activity were not adequately investigated in non-neuronal excitatory cells, where neurotransmitter-based innervation also occurs. We created a mathematical model to replicate the background synaptic noise dynamics in a non-neuronal cell. We utilized the stochastic Ornstein-Uhlenbeck process to represent excitatory synaptic conductance, which was incorporated into a whole-cell model to produce spontaneous and evoked cellular electrical activities. The single-cell model includes many biophysically detailed ion channels represented by a set of ordinary differential equations in Hodgkin-Huxley and Markov formalisms. This paradigm effectively induced irregular spontaneous depolarizations (SDs) and spontaneous action potential (sAP) resembling in vitro-like electrical activity in the cells. The input resistance decreased by multiple factors, and the spontaneous action potential firing rate elevated. The potential to reach the action potential threshold is altered. Background synaptic activity can alter the input/output characteristics of non-neuronal excitatory cells. Suppressing these baseline activities would facilitate the discovery of new pharmaceutical targets for different clinical diseases.

Modeling and assessing the sustainability of machining systems has been considered to be a crucial approach to improving the environmental performance of the machining processes. As the most common machining system, the computer numerical control (CNC) milling system is a typical man-machine cooperative system where the activities of the machine tool and operator generate material and energy consumption. However, the energy consumption of the operator in the CNC milling system has often been ignored in most existing research. Therefore, existing methods fail to provide a comprehensive understanding of the sustainability of the CNC milling system. To fill this gap, an exergy loss assessment method is proposed to investigate the sustainability of the CNC milling system, where the energy consumption of the operator, the energy consumption of the machine tool, and material consumption are taken into consideration. The key performance indexes of the energy consumption of the operator, the energy consumption of the machine tool, the exergy loss, and the specific exergy loss (SEL) are analyzed and modeled. To demonstrate the feasibility of the proposed method, a case study was carried out on a three-axis machining center (XH714D), in which SEL was found to be 88.04J/mm3. The proposed method is effective to assess the sustainability of the CNC milling system, and the established exergy loss models build a good basis for exergy efficiency optimization.

Often, when solving forward, inverse or data assimilation problems, only a part of the solution is needed. As a model, we consider the stationary diffusion problem. We demonstrate an algorithm that can compute only a part or a functional of the solution, without calculating the full inversion operator and the complete solution. It is a well-known fact about partial differential equations that the solution at each discretisation point depends on the solutions at all other discretisation points. Therefore, it is impossible to compute the solution only at one point, without calculating the solution at all other points. The standard numerical methods like a conjugate gradient or Gauss elimination compute the whole solution and/or the complete inverse operator. We suggest a method which can compute the solution of the given partial differential equation 1) at a point; 2) at few points; 3) on an interface; or a functional of the solution, without computing the solution at all points. The required storage cost and computational resources will be lower as in the standard approach. With this new method, we can speed up, for instance, computation of the innovation in filtering or the likelihood distribution, which measures the data misfit (mismatch). Further, we can speed up the solution of the regression, Bayesian inversion, data assimilation, and Kalman filter update problems. Applying additionally the hierarchical matrix approximation, we reduce the cubic computational cost to almost linear $\mathcal{O}(k^2n \log^2 n)$, where $k\ll n$ and $n$ is the number of degrees of freedom. Up to the hierarchical matrix approximation error, the computed solution is exact. One of the disadvantages of this method is the need to modify the existing deterministic solver.

The Stepped Frequency Waveform (SFW) is commonly employed in radar technology to synthesize wideband signals through the aggregation of narrow-band pulses, thereby achieving high-resolution range profiles without the need to increase the radar's instantaneous bandwidth. However, the inherent large time-bandwidth product of SFW introduces substantial ranging errors and energy dispersion, which significantly hinders its efficacy in detecting high-speed objects. This paper introduces a pioneering velocity estimation technique utilizing the fractional Fourier transform (FrFT) to address these limitations. Leveraging the characteristic of the Doppler signal from a moving target, which manifests as a chirp signal with a rate proportional to the target's velocity, the FrFT is utilized for precise velocity estimation. Subsequent to this, velocity compensation is applied using the deduced metrics, followed by the application of the inverse fast Fourier transform (iFFT) to pinpoint the target's exact location. To optimize the computational efficiency of determining the FrFT's optimal order, we propose an iterative algorithm founded on the golden section search method. The effectiveness of the proposed approach is verified by simulation data, and the results demonstrate that the proposed approach can accurately estimate the velocity and the range of the high-speed targets with a relatively low computational complexity.

In this article, we are interested in a new generic class of nonlocal fractional impulsive differential inclusions with linear sectorial operator and Lipschitz multivalued function in the setting of finite dimensional Banach spaces. By modifying the definition of PC-mild solutions initiated by Shu, we succeeded to determine new conditions that sufficiently guarantee the existence of the solutions. The results are obtained by combining techniques of fractional calculus and fixed point theorem for contraction maps. We also characterize the topological structure of the set of solutions. Finally, we provide a demonstration to address the applicability of the theoretical results.

The inhibition of alpha-glucosidase and alpha-amylase is one of clinic strategies for remedy the type II diabetes. Herbal medicines are reported to alleviate hyperglycemia. However, the constituents from those sources whether are targeted to the alpha-glucosidase and alpha-amylase still unexplored. This study attempted to select the compounds for efficacy of hypoglycemia via cellular and mouse levels. The results illustrated that the cytotoxicity in all tested compounds at various concentrations except the concentration of 16-hydroxy-cleroda-3,13-dine-16,15-olide (HCD) at 30 µM were not significant difference (p > 0.05) when compared with the untreated control. Acarbose (reference drug), Antroquinonol, Catechin, Quercetin, Actinodaphnine, Curcumin, HCD, Docosanol, Tetracosanol, Berberine, and Rutin could effectively inhibit the alpha-glucosidase activity of Caco-2 cells when compared with the control (maltose). The compounds (Curcumin, HCD, Tetracosanol, Antroquinonol, Berberine, Catechin, Actinodaphnine, and Rutin) could reduce blood sugar level at 30 min in tested mice. The effects of tested compounds on area under curve (AUC) were significant (p < 0.05) among Acarbose, Tetracosanol, Antroquinonol, Catechin, Actinodaphnine, and Rutin along with Berberine and Quercetin. In in vitro (alpha-glucosidase) with in vivo (alpha-amylase) experiments suggest that bioactive compounds can be a potential inhibitor candidate of alpha-glucosidase and alpha-amylase for the alleviation of type II diabetes.

In this paper we derive a unified perspective for Optimal Transport (OT) theory and Mean Field Control (MFC) theory to analyse the learning process for Neural Networks algorithms in a high-dimensional framework. We consider Mean Field Neural Networks in the context of MFC theory, specifically the mean field formulation of OT theory that allows the development of highly efficient algorithms while providing a powerful tool in the context of explainable Artificial Intelligence.

Microscopic and ultra-microscopic vascular sutures are indispensable in the surgical procedures such as arm transplantation and finger reattachment. The state of the blood vessels after suturing, such as vascular patency, narrow, and blocked, determines the success rate of the operation. If we can grasp the golden window period after blood vessel suture and before muscle tissue suture to achieve accurate and objective assessment of blood vessel status, it can not only reduce medical costs but also improve social benefits. Doppler optical coherence tomography enables high-speed, high-resolution imaging of biological tissues, especially microscopic and ultra-microscopic blood vessels. Using Doppler optical coherence tomography to image the sutured blood vessels, not only the three-dimensional structure of the blood vessels, but also the blood flow information can be obtained. By extracting the contour of blood vessel wall and the contour of blood flow area, the three-dimensional shape of blood vessel can be reconstructed in three dimensions, which provides parameter support for the assessment of blood vessel status. In this work, we propose a neural network-based multi-classification deep learning model that can simultaneously and automatically extract blood vessel boundaries from Doppler OCT vessel intensity images and the contours of blood flow regions from corresponding Doppler OCT vessel phase images. Compared with the traditional random walk segmentation algorithm and cascade neural network method, the proposed model has better performance. This method is easier to realize system integration and has great potential for clinical evaluation. It is expected to be applied to the evaluation of microscopic and ultra-microscopic vascular status in microvascular anastomosis.

Substances that can modify the androgen receptor pathway in humans and animals are entering the environment and food chain with the proven ability to disrupt hormonal systems and leading to toxicity and adverse effects on reproduction, brain development, and prostate cancer, among others. State-of-the-art databases with experimental data of human, chimp, and rat effects by chemicals have been used to build machine learning classifiers and regressors and evaluate these on independent sets. Different featurizations, algorithms, and protein structures lead to dif- ferent results, with deep neural networks (DNNs) on user-defined physicochemically-relevant features developed for this work outperforming graph convolutional, random forest, and large featurizations. The results show that these user-provided structure-, ligand-, and statistically-based features and specific DNNs provided the best results as determined by AUC (0.87), MCC (0.47), and other metrics and by their interpretability and chemical meaning of the descriptors/features. In addition, the same features in the DNN method performed better than in a multivariate logistic model: validation MCC = 0.468 and training MCC = 0.868 for the present work compared to evalu- ation set MCC = 0.2036 and training set MCC = 0.5364 for the multivariate logistic regression on the full, unbalanced set. Techniques of this type may improve AR and toxicity description and predic- tion, improving assessment and design of compounds. Source code and data are available at https://github.com/AlfonsoTGarcia-Sosa/ML

Tumorigenesis is a complex biological phenomenon that includes extensive genetic and phenotypic heterogeneities and complicated regulatory mechanisms. In the recent few years, our studies demonstrate that tumor-initiating cells are similar to neural stem/progenitor cells in regulatory networks, tumorigenicity and pluripotent differentiation potential. In the review, I will make further discussion on these observations and propose a rule of cell biology by integrating these findings with evidence from developmental biology, tumor biology and evolution, which suggests that neural stemness underlies two coupled cell properties, tumorigenicity and pluripotent differentiation potential. Tumorigenicity and phenotypic heterogeneity in tumor is a result of acquirement of neural stemness in cells. The neural stemness property of tumor-initiating cells can hopefully integrate different concepts/hypotheses underlying tumorigenesis. Neural stem cells/neural progenitors and tumor-initiating cells share regulatory networks; both exhibit neural stemness, tumorigenicity and differentiation potential; both are dependent on expression or activation of ancestral genes (the atavistic effect); both rely primarily on aerobic glycolytic metabolism; both can differentiate into various cells or tissues that are derived from three germ layers, resembling severely disorganized or more severely degenerated process of embryonic development; both are enriched in long genes with more splice variants that provide more plastic scaffolds for cell differentiation, etc. The property of neural stemness might be a key point to understand tumorigenesis and pluripotent differentiation potential, and possibly explain certain pathological observations in tumors that have been inexplicable. Therefore, behind the complexity of tumorigenesis might be a general rule of cell biology, i.e., neural stemness represents the ground state of cell tumorigenicity and pluripotent differentiation potential.

This study develops a predictor-corrector algorithm for the numerical simulation of IVPs involving singular generalized fractional derivatives with Mittag-Leffler kernels. The proposed algorithm converts the considered IVP into a Volterra-type integral equation and then uses Trapezoidal rule to obtain approximate solutions. Numerical approximate solutions of some singular generalized fractional derivative with Mittag-Leffler kernels models have been presented to demonstrate the efficiency and accuracy of the proposed algorithm. The algorithm describes the influence of the fractional derivative parameters on the dynamics of the studied models. The suggested method is expected to be effectively employed in the field of simulating generalized fractional derivative models

Convolutional Neural Networks (CNNs) are often criticized for their lack of transparency, acting as 'black boxes' in decision-making, a challenge compounded by class imbalance in ECG datasets, which limits their clinical application. This study introduces a CNN-based ECG signal classification model that enhances interpretability and addresses class imbalance through the Synthetic Minority Over-sampling Technique (SMOTE). The model also integrates Uniform Manifold Approximation and Projection (UMAP) for dimensionality reduction and SHAP value analysis, facilitating the visualization of decision boundaries and the assessment of feature contributions. Our evaluation using the MIT-BIH Arrhythmia Database highlights the model's high performance, with accuracy and precision nearing 1.00 for Normal ECG (NOR), Left Bundle Branch Block (LBBB), Right Bundle Branch Block (RBBB), and Ventricular Premature Beat (PVC) in the six-class task. In the ten-class task, the model demonstrated robustness, particularly with an accuracy of 0.9846, precision of 0.9783, recall of 0.9736, and F1 score of 0.9760 in Pacemaker Fusion Beat (PFHB), supported by an AUC of 0.9999 and AP of 0.9885. These results underscore the model's efficacy in cardiac rhythm recognition and resilience to class imbalance. Future research will explore sophisticated model architectures and feature extraction methods to enhance the model's generalization and clinical applicability for early heart disease diagnosis and personalized treatment.

Objectives: Few studies in literature evaluate the "mean measure" of root divergence. Most of them are linear measurements, they hardly describe the dental furcation conformation. It is left to the subjectivity of the operator deciding whether a furcation is convergent or divergent. The goal of this study is to create a visual evaluation method to overcome these problems giving a conformation of the entire interradicular space. Material and methods: A user-friendly software (Paint®, Windows10®) was used to measure endo-oral radiographs of upper and lower molars. Three kinds of measurements were taken. Three operators used the software to measure 20 radiographs, then the technique was repeated on 250 radiographic images to identify an average measurement. The ratio of these three measurements allowed to develop a new visual evaluation method of the interradicular space. Results: Intra and inter-operator reproducibility was statistically assessed on a sample of 20 anonymous endo-oral radiographs measured by 3 blind operators. Then, a sample of 250 anonymous endo-oral radiographs were measured by a blind operator and were statistically evaluated to identify an average value to define a main conformation of the interradicular space. Measurements made by the 3 operators on the 20 radiographic images showed that the technique is reproducible, and a mean value of the interradicular space was obtained. Conclusions: A new anatomical evaluation of the interradicular space in its entirety, which could help the clinicians in the therapy of furcated molars, can be obtained.

The emergence of the semiconductor industry in the early 1960s resulted in a significant stage in the evolution of computing when large computational problems, as typified by the application of the discrete Fourier transform (DFT) to the task of spectrum estimation, could suddenly, with the availability of suitable algorithms, be solved in close to real time fashion. This paper provides a brief and meandering account of the history of the DFT’s various solutions, referred to generically as the fast Fourier transform (FFT), the algorithm being chosen for its mathematical elegance, practical significance and ever‑increasing range of applications. We touch upon a few of the most striking personalities, places and events that were encountered along the way and look, in particular, at the recent British contribution to the journey.

Polyhedral Oligomeric Silsesquioxanes (POSS) are one of the smallest silica nano particles. The presence of ordered ladder-like or cage conformation in their structure leads to remarkable thermal stability far greater than that for a linear polysiloxane. Reinforcement with nano particles is one of the recently favored strategy used to enhance the performance of polymers materials. The cyclic silica structure present in POSS ensures excellent thermal and mechanical stability. As a reinforcing filler, POSS can enhance the resistance of polymer matrix against pyrolysis and corrosion. In this paper, amine-terminated POSS with ladder like structure was synthesized by condensation of hydrolyzed aminosilane coupling agent. The ladder-like structure of POSS severely limits the motion of the chain backbone. The absence of phase transition for the synthesized POSS was confirmed by differential scanning calorimetry (DSC). Thermogravimetric analysis (TGA) was utilized to evaluate the thermal stability of POSS. TGA data show that the ladder-like POSS reported here has high char yield of about 75 % in nitrogen atmosphere and 54% in air atmosphere at 800℃. The TGA derivative curves show that the degradation of ladder-like POSS involves multiple stages and that the degradation rate is directly proportional to the heating rate. With the aid of Fourier Transform Infrared Spectroscopy (FT-IR), the cyclic structure of Si-O-Si bonding was determined to be the predominant structure. By analyzing the FTIR spectra of the cured POSS residue obtained at the specified temperatures, the detailed degradation mechanism of POSS was inferred. From the FTIR spectra of the low temperature cured samples, it was shown that the terminal silanol group was eliminated below 400℃. Some intermediate polymeric siloxane structures were observed by means of FT-IR and they eventually transitioned into silica which is the final product of pyrolysis of POSS. The presence of the FTIR transmission peaks at 1000 and 1100 cm-1, due to asymmetrical vertical and horizontal stretching of Si-O-Si, were the key evidence for the inferred ladder-like structure of POSS.