The current work reveals the fine tuning between stability zones and randomness of Pointwise Stationary Fluid Flow Approximation (PSFFA) model of the non-stationary queueing D/M/1 system. More specifically, this clearly provides more insights into developing a contemporary PSFFA theory that unifies non-stationary queueing theory with chaos theory and fields in both theoretical physics and chaotic systems. This opens new grounds for stability analysis of non-stationary queueing systems.

This paper provides the first-time ever analytic modelling for Pointwise Stationary Fluid Flow Approximation(PSFFA) model of the non-stationary

This paper numerically investigates a 3D mesh independency study of a straight blade horizontal axis tidal turbine modelled using Computational Fluid Dynamics (CFD). The solution was produced by employing two turbulence models, the standard k-ε model and Shear Stress Transport (SST) in ANSYS CFX. Three parameters were investigated: mesh resolution, turbulence model, and power coefficient in the initial CFD, analysis. It was found that the mesh resolution and the turbulence model affect the power coefficient results. The power coefficients obtained from the standard k-ε model are 15% to 20% lower than the accuracy of the SST model. It can also be demonstrated that the torque coefficient increases with the increasing Tip Speed Ratio (TSR), but drops drastically after TSR = 5 and k-ε model failing to capture the non-linearity in the torque coefficient with the increasing TSR.

The aim of this work is to analyze and investigate the shape preserving properties of ternary 4-point non-stationary interpolating subdivision schemes constructed by Beccari et al. [1] with a tension parameter !k+1 which can reproducing exponential. Moreover, the conditions on the initial control points are developed that allow user to generate shape preserving limit curves after a nite number of subdivision steps and generalize these results in limiting case. Signicance of derived conditions are illustrated through graphs and the whole discussion is followed by examples.

In this paper, Lyapunov-Razumikhin technique, design of state-dependent switching laws, a fixed point theorem and variational methods are employed to derive the existence and the unique existence results of (globally) exponentially stable positive stationary solution of delayed reaction-diffusion cell neural networks under Dirichlet zero boundary value, including the global stability criteria \textbf{in the classical meaning}. Next, sufficient conditions are proposed to guarantee the global stability invariance of ordinary differential systems under the influence of diffusions. New theorems show that the diffusion is a double-edged sword in judging the stability of diffusion systems. Besides, an example is constructed to illuminate that any non-zero constant equilibrium point must be not in the phase plane of dynamic system under Dirichlet zero boundary value, or it must lead to a contradiction. Next, under Lipschitz assumptions on active function, another example is designed to prove that the small diffusion effect will cause the essential change of the phase plane structure of the dynamic behavior of the delayed neural networks via a Saddle point theorem. Finally, a numerical example illustrates the feasibility of the proposed methods.

The current work reveals the fine tuning between stability zones and randomness of GI/M/1 Pointwise Stationary Fluid Flow Approximation (PSFFA) model of the non-stationary D/M/1 queueing system. More specifically, this clearly provides more insights into developing a contemporary PSFFA theory that unifies non-stationary queueing theory with chaos theory and fields in both theoretical physics and chaotic systems. This opens new grounds for stability analysis of non-stationary queueing systems. A notable application of GI/M/1 queueing model to achieve ultra-low latency of autonomous driving service is highlighted. Concluding remarks associated with future avenues of research are given.

The Doppler band compensated by the keystone transform (KT) is limited. Therefore, it needs to be used in conjunction with the Doppler ambiguity compensation function to correct the range migration (RM) caused by maneuvering targets with Doppler ambiguity. However, the KT implemented by sinc interpolation suffers from significant performance loss at boundaries of compensation Doppler bands. Additionally, in a multi-target scenario, KT implementation methods occupy high complexity when the Doppler range of targets spans over two compensation Doppler bands. To address aforementioned issues, this study presents a variable Doppler starting point keystone transform (VDSPKT) method, where a new form of ambiguity compensation function is constructed, turning the Doppler starting point of the compensation band in KT variable. Firstly, the position of the compensation Doppler band is changed from fixed to adjustable as needed, enhancing the flexibility of KT. Crucially, the connection points of the compensation Doppler bands in sinc interpolation are reset, avoiding the performance loss at their boundaries. Also, the compensation band is adjusted to cover the narrow Doppler frequency range caused by targets, significantly improving the computational efficiency. Finally, the simulation results demonstrate that the proposed approach effectively addresses the performance degradation and high computational complexity of KT in the aforementioned scenarios, resulting in a computational load reduced by approximately 50% compared to traditional methods.

Panel data of our interest consist of a moderate number of panels, while the panels contain a small number of observations. An estimator of common breaks in panel means without a boundary issue for this kind of scenario is proposed. In particular, the novel estimator is able to detect a common break point even when the change happens immediately after the first time point or just before the last observation period. Another advantage of the elaborated change point estimator is that it results in the last observation in situations with no structural breaks. The consistency of the change point estimator in panel data is established. The results are illustrated through a simulation study. As a by-product of the developed estimation technique, a theoretical utilization for correlation structure estimation, hypothesis testing, and bootstrapping in panel data is demonstrated. A practical application to non-life insurance is presented as well.

We generalize the point information gain (PIG) and derived quantities, i.e., point information gain entropy (PIE) and point information gain entropy density (PIED), for the case of the Rényi entropy and simulate the behavior of PIG for typical distributions. We also use these methods for the analysis of multidimensional datasets. We demonstrate the main properties of PIE/PIED spectra for the real data on the example of several images, and discuss further possible utilizations in other fields of data processing.

The task of weakly supervised point cloud semantic segmentation has received widespread attention and also has been widely used in autonomous driving, robotics, and modern industries. Due to the high dimensionality and large volume of point cloud data, many technical difficulties appeal to weakly supervised semantic processing, especially segmentation. However, weakly-supervised schemes usually provide only partial labelling information of the underlying point cloud data and thus need to effectively extract local features, geometric information, and contextual relationships only using these limited labelled data for supervised learning. To improve weakly-supervised semantic segmentation, we propose a novel segmentation network through the boundary-based feature aggregation based on a K-NN algorithm with down-sampling operation, and also introduce the smoothness loss and Siamese loss for effective segmentation. The experiments on public datasets demonstrate that our presented segmentation method exceeds most of the existing fully supervised and weakly-supervised methods in terms of mIoU. Specifically, our network has high segmentation accuracy on the labels of objects with similar geometrical structures, such as ceiling, wall, floor, chair and table, reaching 91.2%, 98.8%, 83.3%, 75.3% and 80.2%, respectively. Extensive experiments also illustrate its robustness, effectiveness, and generalization of the proposed weakly supervised segmentation network.

Aiming at effectively generating safe and reliable motion paths for quadruped robots, a hierar-chical path planning approach driven by dynamic 3D point cloud is proposed in this article. The developed path planning model is essentially constituted of two layers: global path planning layer and local path planning layer. At the global path planning layer, a new method is proposed for calculating terrain potential field based on point cloud height segmentation. Variable step size is employed to improve the path smoothness. At the local path planning layer, a real-time prediction method for potential collision area and a strategy for temporary target point selection is developed. Quadruped robot experiments were carried out in an outdoor complex environment. The experi-mental results verified that, for global path planning, the smoothness of the path is improved and the complexity of the passing ground is reduced. The effective step size is increased by a maxi-mum of 13.4 times, and the number of iterations is decreased by up to 1/6, compared with the traditional fixed step size planning algorithm. For local path planning, the path length is short-ened by 20%, more efficient dynamic obstacle avoidance and more stable velocity planning are achieved by using the improved dynamic window approach (DWA).

A semi–numerical approach proposed many years ago for describing gravitational collapse in the post–quasi–static approximation , , , , is modified in order to avoid the numerical integration of the basic differential equations the approach is based upon. For doing that we have to impose some restrictions on the fluid distribution. More specifically, we shall assume the vanishing complexity factor condition, which allows for analytical integration of the pertinent differential equations and leads to physically interesting models. Instead, we show that neither the homologous nor the quasi–homologous evolution are acceptable since they lead to geodesic fluids, which are unsuitable for being described in the post–quasi–static approximation. Also, we prove that, within this approximation, adiabatic evolution also leads to geodesic fluids and therefore we shall consider exclusively dissipative systems. Besides the vanishing complexity factor condition, additional information is required for a full description of models. We shall propose different strategies for obtaining such an information, which are based on observables quantities (e.g. luminosity and redshift), and/or heuristic mathematical ansatz. To illustrate the method, we present two models. One model is inspired in the well known Schwarzschild interior solution, and another one is inspired in Tolman VI solution.

The prevalence of hepatitis B and delta viruses (HBV/HDV) among people who use drugs (PWUD) remains largely unknown. In the context of one Philadelphia-based harm reduction organization (HRO), this study aimed to assess HBV/HDV prevalence and facilitate linkage to care. Participants completed a demographic HBV/HDV risk factor survey and were screened for HBV and reflexively for HDV if positive for HBV surface antigen or isolated core antibody. Fisher’s exact tests and regression were used to understand relationships between risks and HBV blood markers. Of the 498 participants, 126 (25.3%) were susceptible to HBV, 52.6% had been vaccinated against HBV, and 17.9% had recovered from a past infection. Eleven (2.2%) participants tested positive for isolated HBV core antibody, 10 (2.0%) for HBV surface antigen, and one (0.2%) for HDV antibody. History of incarceration was associated with current HBV infection, while transactional sex and experience of homelessness were predictive of previous exposure. This study found high rates of current and past HBV infection, and a 10% HBV/HDV co-infection rate. Despite availability of vaccine, one quarter of participants remained vulnerable to infection. Findings demonstrate the need to improve low-threshold HBV/HDV screening, vaccination, and linkage to care among PWUD. The study also identified gaps in the HBV/HDV care cascade, including lack of point-of-care diagnostics and lack of support for HROs to provide HBV services.

Artificial intelligence (AI) is increasingly being used to improve the quality control of point-of-care diagnostics. This is caused by a number of factors, including the following: 1. AI can accelerate and improve testing accuracy. In comparison to humans, AI technology can review data more quickly and precisely, reducing errors and improving overall quality assurance. 2. When it comes to improving POC test findings on healthcare issues such as infectious diseases or medical crises such as heart attacks, AI can be used for sophisticated predictive analytics and modeling that aid in better decision-making. 3. Artificial intelligence facilitates process automation, increasing productivity and lowering labor costs in labor-intensive tasks such as testing and analyzing samples collected at point-of-care facilities. 4. The use of AI enables organizations implementing these solutions to gain insights from large volumes of raw diagnostic data generated faster and more accurately, allowing them to build solid frameworks around preventive care initiatives and significantly influence public health outcomes.5. Artificial intelligence (AI) has been demonstrated to be a useful tool for real-time monitoring systems that identify any problems with test results early so that they can be corrected before affected patients receive inaccurate diagnoses or treatment plans based on false information provided by diagnostic tests performed at points of care such as clinics or hospitals.Using these technologies would allow healthcare organizations to spend less on labor while still receiving exact diagnoses and rapid treatment delivery at a fraction of the cost that manual approaches required earlier.

In order to deal with imprecision, ambiguity, and uncertainty in data analysis, Pawlak introduced rough set theory in 1982. This paper aims to expand the scope of basic set theory developed by presenting the notions of δP-upper and δP-lower approximations, that are based on the notion of δP-open sets, we additionally examine a few of their fundamental characteristics.

The research of object classification and part segmentation is a hot topic in computer vision. A considerable number of studies have been carried out about deep learning on 3D point clouds. However,it is challenging to achieve effective feature learning due to sparsity of point clouds. Recently, a variety of Transformers have been adopted to improve point cloud processing and display great potential. Nevertheless, large numbers of Transformer layers tend to incur huge computational and memory costs. PointNet++ is one of the most influential neural architectures for point cloud understanding. Although the accuracy of PointNet++ has been largely surpassed by recent networks, this does not mean that PointNet++ has no potential.Thus, this paper offer two major contributions that significantly improve PointNet++ performance. Firstly, we introduce a novel contextual feature extraction (CFE) block that significantly enhances the feature extraction capabilities of PointNet++ networks. Secondly, to further enhance feature fusion, we seamlessly integrate a mutual learning (ML) block into the network architecture. By embedding these two innovative blocks within each layer of the network, we not only enrich the network's functionality but also impart it with greater robustness and adaptability. The specific experiments were conducted on the S3DIS (6-fold cross-validation) and Modelnet40 datasets with 86.5% and 92.7% accuracy, respectively, which proved that our model is comparable or even better than most existing methods for classification and segmentation tasks.

This paper provides a new discovery that adds to the contemporary theory of modelling of non-stationary queues, by capturing analytically the behavior of the root parameter, for the G1/M/1 PSFFA model of non-stationary Ek/M/1 queue. Additionally, it has been also revealed that the resulting root parameter reduces to the PSFFA model of non-stationary queue. Potential applications of PSFFA to Computer engineering are provided. Some challenging open problems are addressed combined with closing remarks and future research directions.

Given a fuzzy normed space $ \left( X,N \right) $‎, ‎we will introduce the notion of fuzzy near best approximation within a relative distance $ \rho \geq 0 $‎. ‎Some basic properties are characterized and also many examples for illustration are presented‎.

Social media platforms have been entirely an undeniable part of the lifestyle for the past decade. Analyzing the information being shared is a crucial step to understanding human behavior. Social media analysis aims to guarantee a better experience for the user and risen user satisfaction. However, first, it is necessary to know how and from which aspects to compare users. In this paper, an intelligent system has been proposed to measure the similarity of Twitter profiles. For this, firstly, the timeline of each profile has been extracted using the official TwitterAPI. Then, all information is given to the proposed system. Next, in parallel, three aspects of a profile are derived. Behavioral ratios are time-series-related information showing the consistency and habits of the user. Dynamic time warping has been utilized for the comparison of the behavioral ratios of two profiles. Next, the audience network is extracted for each user, and for estimating the similarity of two sets, Jaccard similarity is used. Finally, for the Content similarity measurement, the tweets are preprocessed respecting the feature extraction method; TF-IDF and DistilBERT for feature extraction are employed and then compared using the cosine similarity method. Results have shown that TF-IDF has slightly better performance; therefore, the more straightforward solution is selected for the model. Similarity level of different profiles. As in the case study, a Random Forest classification model was trained on almost 20000 users revealed a 97.24% accuracy. This comparison enables us to find duplicate profiles with nearly the same behavior and content.

Poultry farming in Slovakia has a tradition and an irreplaceable position to ensure rational nutrition for the population. In terms of a nutritional value, poultrymeat (Galliformes) contains a high amount of proteins, essential amino acids, essential unsaturated fatty acids, minerals, vitamins and a low fat content. Poultrymeat production has a relatively short reproductive cycle and thus allows regulating the demand and supply. The poultry market also influences the development of domestic consumption. According to the Statistical Office of the Slovak Republic, the consumption of meat has witnessed a persistent increase over the last 10 years. [1] According to the 2023 AVEC (The Voice of European Meat Sector) annual report, the consumption of poultrymeat in Slovakia was 20.0 kg per person per year. The average consumption in the EU-27 (2021) was 23.4 kg, with the countries with the highest consumption being Portugal (37.8 kg), Ireland (36.0 kg), Hungary (33.5 kg) and Spain (29.9 kg). On the other hand, the countries with the lowest consumption of poultrymeat, apart from Slovakia, also include Austria and Greece with a consumption of 21.5, resp. 21.0 kg [2]. The breeding of broiler chickens, as well as the production and placing on the market of poultrymeat must comply with the requirements laid down by legislation, while the compliance is regularly checked by the competent authorities.

One of the solutions of the Einstein equations, called McVittie solution, signifying a black hole embedded by the dynamic spacetime is studied. In the stationary spacetime the Mcvittie metric becomes the Schwarzschild-de Sitter metric (SdS). The geodesic of a freely falling test particle towards the black hole is examined in the SdS spacetime. It is found that unlike Schwarzschild case the potential of such particle becomes maximum at a point where it eventually stops to follow an unstable circular motion and then resumes its motion towards black hole center. It is shown that an observer or system of particles is spaghettified near the black hole singularity in the SdS spacetime. The dynamic of the universe in the framework of McVittie metric, being a generalized time dependent SdS solution, is represented in terms of that point, called stationary or turning point. The motion of the stationary point is studied in various regimes of the expanding universe and the possible outcomes are discussed in brief.

For multi-sensor integrated systems, such as a mobile mapping system (MMS), data fusion at sensor-level, i.e., the 2D-3D registration between optical camera and LiDAR, is a prerequisite for higher level fusion and further applications. This paper proposes a line-based registration method for panoramic images and LiDAR point cloud collected by a MMS. We first introduce the system configuration and specification, including the coordinate systems of the MMS, the 3D LiDAR scanners, and the two panoramic camera models. We then establish the line-based transformation model for panoramic camera. Finally, the proposed registration method is evaluated for two types of camera models by visual inspection and quantitative comparison. The results demonstrate that the line-based registration method can significantly improve the alignment of the panoramic image and LiDAR datasets under either the ideal spherical or the rigorous panoramic camera model, though the latter is more reliable.

Hasselmann and coauthors proposed the discrete interaction approximation (DIA) as the best tool replacing the nonlinear evolution term in a numerical wind-wave model. Much later, Polnikov and Farina radically improved the original DIA by means of location all the interacting four wave vectors, used in the DIA configuration, exactly at the nodes of the numerical frequency-angular grid. This provides nearly two-times enhancing the speed of numerical calculation for the nonlinear evolution term in a wind-wave model. For this reason, the proposed version of the DIA was called as the fast DIA (FDIA). In this paper we demonstrate all details of the FDIA concept for several frequency-angular numerical grids of high resolution, with the aim of active implementation the FDIA in modern versions of world-wide used wind-wave models.

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.

Boltzmann codes are essential tools for studying cosmology. Most of the codes are based on a seminal work by Ma and Bertschinger. We found that the formalism employed in those codes has at least three possible problems which need to be understood. i) The equation of motion for baryons are gauge incompatible, ii) they break the Bianchi identity, and iii) it is not clear from the equations of motion which physical system is considered. In this work we revisit the baryon physics and address all the above mentioned issues, based solely on conservation of stress-energy tensor, resulting in taking into account a correction that is usually neglected and that is numerically small. We also study the tight coupling approximation up to the second order without choosing any gauge. We implement the improved baryon equations in a Boltzmann code and investigate the change in the estimate of cosmological parameters by performing an MCMC analysis. While in this paper we study the Lambda-CDM model only, our baryon equations can be easily implemented in other models and various modified gravity theories.

The wave energy converter (WEC) technology constantly develops new designs and models. To encourage its development within the energy sector, research is required to improve current designs and create durable and effective devices. However, it is also crucial to investigate the suitability of a WEC to a site-specific sea condition as this can impact its optimal power absorption and constructability. This study evaluates and compares the efficiency of a heaving buoy with varied geometries in one of the most energetic places along the Mexican coast. A statistical analysis of the wave climate on the coast of Ensenada during the last 42 years is performed to define the conditions to which the device is subjected. The location of the WEC in shallow waters is chosen using a computational model which solves the modified mild slope equation in its elliptic shape. The heaving buoy floater is studied using three distinct geometries: a semi-sphere, a cylinder, and a proposed rounded semi-rectangle. The hydrodynamic response of the three geometries is then analysed in the frequency and time domain using ANSYS AQWA. The hydrodynamic study involves the assessment of the floating body dynamics, exerted forces, the power absorbed as well as the suitability of the proposed power take-off (PTO) system. Findings reveal that the proposed geometry absorbs the most energy, with an annual power of 135.11 MW, and that the transmission PTO design is appropriate for this type of technology.

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.

We develop an 1/n expansion method for the systematic approxi- mation of the solutions of classical spin systems (tri-dimensional vec- tors) which can describe general spin-spin interactions and phases with complex magnetization pattern. This method is applied to study the phase transitions observed in pyrochlore crystals (e.g. Gd₂ Ti₂ O₇ ) and the results have qualitative agreement with the experimental ones.

Purpose of this article is to introduce a modification of Phillips operators on the interval $\left[ \frac{1}{2},\infty \right) $ via Dunkl generalization. This type of modification enables a better error estimation on the interval $\left[ \frac{1}{2},\infty \right) $ rather than the classical Dunkl Phillips operators on $\left[ 0,\infty \right) $. We discuss the convergence results and obtain the degrees of approximations. Furthermore, we calculate the rate of convergence by means of modulus of continuity, Lipschitz type maximal functions, Peetre's $K$-functional and second order modulus of continuity.

Purpose of this article is to introduce a modification of Phillips operators on the interval $\left[ \frac{1}{2}% ,\infty \right) $ via Dunkl generalization. This type of modification enables a better error estimation on the interval $\left[ \frac{1}{2},\infty \right) $ rather than the classical Dunkl Phillips operators on $\left[ 0,\infty \right) $. We discuss the convergence results and obtain the degrees of approximations. Furthermore, we calculate the rate of convergence by means of modulus of continuity, Lipschitz type maximal functions, Peetre's $K$-functional and second order modulus of continuity.

This paper proposes a novel single-stage buck-boost three-Level neutral-point-clamped (NPC) inverter with two independent dc sources coupled for the grid-tied photovoltaic (PV) application, which can effectively solve the unbalanced operational conditions generally appeared between two coupled independent PV sources induced by the unequal irradiation and temperature distribution. The proposed control scheme can simultaneously guarantee the maximum power point (MPP) operation of both PV sources and maintain the output waveform quality. Compared to the traditional two-stage PV inverter, the proposed NPC inverter could reduce the PV array voltage requirement and dc-link capacitors’ voltage rating, meanwhile show the advantage in operational efficiency. MATLAB simulations and the captured experimental results are presented to show the performance of the proposed three-level inverter.

The aim of this work is to introduce new ways to model the I-V characteristic of a PV cell or PV module using straight lines and Bézier curves. This is a complete novel approach, Bézier curves being previously used mainly for computer graphics. The I-V characteristic is divided in three sections, modeled with lines and a quadratic Bézier curve in the first case and with three cubic Bézier curves in the second case. The result proves to be accurate and relies on the fundamental points usually present in the PV cell datasheets: Voc (the open circuit voltage), Isc (the short circuit current), Vmp (the maximum power corresponding voltage) and Imp (the maximum power corresponding current) and the parasitic resistances Rsh0 (shunt resistance at Isc) and Rs0 (series resistance at Voc). The proposed algorithm completely defines all the implied control points and the error is analyzed. The temperature and irradiance influence is also analyzed. The model is also compared using the least squares fitting method. The final validation shows how to use Bézier cubic curves to accurately represent the I-V curves of an extensive range of PV cells and arrays.

The purpose of this paper is threefold: (i) to introduce and study the Euler-Lagrange prolongations of flatness PDEs solutions (best approximation of flatness) via associated least squares Lagrangian densities and integral functionals on Riemannian manifolds; (ii) to analyze some decomposable multivariate dynamics represented by Euler-Lagrange PDEs of least squares Lagrangians generated by flatness PDEs and Riemannian metrics; (iii) to give examples of explicit flat extremals and non-flat approximations.

In this review paper, we present a pellucid proof of how x tanh(x/µ) approximates |x|and is better than √x² +µ  when we are concernedwith accuracy.

Recommendation systems are crucial in navigating the vast digital market. However, user data’s dynamic and non-stationary nature often hinders their efficacy. Traditional models struggle to adapt to the evolving preferences and behaviours inherent in user interaction data, posing a significant challenge for accurate prediction and personalisation. Addressing this, we propose a novel theoretical framework, the Non-stationary Transformer, designed to capture and leverage the temporal dynamics within data effectively. This approach enhances the traditional transformer architecture by introducing mechanisms accounting for non-stationary elements, offering a robust and adaptable solution for recommendation systems. Our experimental analysis, encompassing deep learning and reinforcement learning paradigms, demonstrates the framework’s superiority over benchmark models. The empirical results confirm the efficacy of our proposed framework, which not only provides significant performance enhancements, approximately 8% in Logloss reduction and up to 2% increase in F1 score but also underscores its potential applicability across accumulative reward scenarios. These findings advocate adopting Non-stationary Transformer models to tackle the complexities of today’s recommendation tasks.

The current paper is devoted to the introduction of simpler Eulerian variational principles from which all the relevant equations of non-barotropic stationary magnetohydrodynamics can be derived for magnetic fields which lie on surfaces. A variational principle is given in terms of three independent variables for stationary non-barotropic magnetohydrodynamic flows. This is a smaller number of variables than the eight variables which appear in the standard equations of non-barotropic magnetohydrodynamics which are the magnetic field, the velocity field, the specific entropy and the density. We further investigate the case in which the flow along magnetic lines is not ideal.

Bartonella henselae is a fastidious Gram-negative intracellular bacterium which can cause cat scratch disease, endocarditis in humans and animals as well as other complications, leading to acute or chronic infections. The current treatment for Bartonella infections is not very effective due to antibiotic resistance and also persistence. To develop better therapies for persistent and chronic Bartonella infections, in this study, with the help of SYBR Green I/PI viability assay, we performed a high-throughput screening of an essential oil library against stationary phase B. henselae. We successfully identified 32 essential oils that had high activity, including four essential oils extracted from Citrus plants, three from Origanum, three from Cinnamomum, two from Pelargonium and two from Melaleuca, as well as frankincense, ylang ylang, fir needle, mountain savory (winter), citronella, spearmint, elemi, vetiver, clove bud, allspice and cedarwood essential oils. The minimal inhibitory concentration (MIC) determination of these 32 top hits indicated they were not only active against stationary phase non-growing B. henselae but also had good activity against log phase growing B. henselae. The time-kill curve by drug exposure assay showed 13 active hits, including essential oils of oregano, cinnamon bark, mountain savory (winter), cinnamon leaf, geranium, clove bud, allspice, geranium bourbon, ylang ylang, citronella, elemi and vetiver, could eradicate all stationary phase B. henselae cells within 7 days at the concentration of 0.032% (v/v). Two active ingredients, carvacrol and cinnamaldehyde, of oregano and cinnamon bark essential oils, respectively, were shown to be very active against stationary phase B. henselae such that they were able to eradicate all the bacterial cells even at the concentration ≤ 0.01% (v/v). Our finding of active essential oils may help to develop more effective treatments for persistent Bartonella infections.

The influence of the grain structure on the tensile deformation strength is studied for precipitation-strengthened Cu-0.2%Zr at 673 K. Subgrains and grains are formed by ECAP and annealing. The fraction of high-angle boundaries increases with prestrain. Subgrains and grains coarsen during deformation. This leads to softening in the quasi-stationary state. The initial quasi-stationary state of severely predeformed, ultrafine-grained material exhibits relatively high rate-sensitivity at relatively high stresses. This is interpreted as result of the stress dependences of the quasi-stationary subgrain size and the volume fraction of subgrain-free grains.

The fractional derivatives are a generalization the derivatives of integer order and find applications in studying memory processes in various scientific fields. Numerical methods are used to solve and analyze fractional models of real world problems. In this paper, we consider an approximation of the Caputo fractional derivative and its asymptotic formula, whose generating function is the polylogarithmic function. In the paper, we prove the convergence of the approximation and derive an estimate for the error and order. We consider an application of the approximation for the construction of finite difference schemes for numerical solution of the two-term ordinary fractional differential equation and the time-fractional Black-Scholes equation for option pricing. The properties of the approximation are used to prove the convergence of the methods used for numerical solution of the fractional differential equations. The theoretical results for the error and order of the methods are illustrated by the results of numerical experiments.

In this study, we propose an augmentation method for machine learning based on relabeling data in caregiving and nursing staff indoor localization with Bluetooth Low Energy (BLE) technology. Indoor localization is used to monitor staff to patient assistance in caregiving and to gain insights into workload management. However, improving accuracy is challenging when there is a limited amount of sensor data available for training. In this paper, we propose a data augmentation method to reuse the Received Signal Strength (RSS) from different sensors by relabeling to the sensors with less samples resolving data imbalance. Standard deviation and Kullback-Leibler divergence between minority and majority class are used to measure signal pattern to find matching sensors to relabel. By matching sensors between classes, two variation of relabeling are implemented specifically full and partial matching. The performance is evaluated using real world dataset we collected for five days in a nursing care facility installed with 25 BLE beacons. Random Forest model is utilized for location recognition, and performance is compared using the weighted F1-score to account for class imbalance. By increasing the sensor data with our proposed relabeling method for data augmentation, we achieved higher minority class F1-score as compared to augmentation with Random Sampling, Synthetic Minority Oversampling Technique (SMOTE) and Adaptive Synthetic Sampling (ADASYN). Our proposed method utilizes collected sensor data by leveraging majority class samples. Full matching demonstrated a 6 to 8% improvement from the original baseline overall weighted F1-score.

The point cloud is a form of three-dimensional data that comprises various detailed features at multiple scales. Due to this characteristic and its irregularity, point cloud analysis based on deep learning is challenging. While previous works utilize the sampling-grouping operation of PointNet++ for feature description and then explore geometry by means of sophisticated feature extractors or deep networks, such operations fail to describe multi-scale features effectively. Additionally, these techniques have led to performance saturation. And it is difficult for standard MLPs to directly "mine" point cloud. To address above problems, we propose the Detail Activation (DA) module, which encodes data based on Fourier transform after sampling and grouping. We activate the channels at different frequency levels from low to high in the DA module to gradually recover finer point cloud details. As training progresses, the proposed Point-MDA can uncover local and global geometries of point cloud progressively. Our experiments show that Point-MDA achieves superior classification accuracy, outperforming PointNet++ by 3.3% and 7.9% in terms of overall accuracy on the ModelNet40 and ScanObjectNN dataset, respectively. Furthermore, it accomplishes this without employing complicated operations, while exploring the full potential of PointNet++.

A software defined radio (SDR) is a communication system that makes use of components that can be configured through software, in contrast to traditional systems where these components are variable through hardware, these radio devices are much more versatile, this article describes the factors that must be considered when implementing a communication system based on Software Defined Radios (SDR), in order to reduce the attenuation factors and thus obtain the maximum distance for a transmission of data effectively in the UHF band. The calculations made for the first Fresnel zone and for the design of the Ground Plane type antennas used in the transmission/reception stages of the x40 bladeRF platforms are also presented. The tests were carried out at the facilities of the Huarangal Nuclear Center of the Peruvian Institute of Nuclear Energy, obtaining favorable results that allow ratifying the versatility and performance of the SDRs.

Model-based image reconstruction has brought improvements in terms of contrast and spatial resolution to imaging applications such as magnetic resonance imaging and emission computed tomography. However, their use for pulse-echo techniques like ultrasound imaging is limited by the fact that model-based algorithms assume a finite grid of possible locations of scatterers in a medium -- which does not reflect the continuous nature of real world objects and creates a problem known as off-grid deviation. To cope with this problem, we present a method of dictionary expansion and constrained reconstruction that approximates the continuous manifold of all possible scatterer locations within a region of interest. The expanded dictionary is created using a highly coherent sampling of the region of interest, followed by a rank reduction procedure based on a truncated singular value decomposition. We develop a greedy algorithm, based on the Orthogonal Matching Pursuit (OMP), that uses a correlation-based non-convex constraint set that allows for the division of the region of interest into cells of any size. To evaluate the performance of the method, we present results of 2-dimensional ultrasound image reconstructions with simulated data in a nondestructive testing application. Our method succeeds in the reconstructions of sparse images from noisy measurements, providing higher accuracy than previous approaches based on regular discrete models.

This study investigates the valorization potential of yellowfin tuna tails for the production of high-value commercial products. Muscle and skins were firstly mechanically separated by using a specifically designed device. The muscle was then used as a nitrogen source for the growth of the proteolytic enzymes-producer Bacillus subtilis, whereas the skins were employed for gelatin extrac-tion. The proteases from Bacillus subtilis were partially purified and used to produce antioxidant peptides from gelatin obtained. The gelatin obtained formed a gel upon cooling, with gelling and melting temperatures at 16 ºC and 22 ºC, respectively, and Bloom Strength of ≈ 160. RSM was used to determine the optimal hydrolysis conditions to obtain the highest antioxidant activity (35.96%, measured as DPPH radical scavenging activity), which were 50°C / 6.5 IU of enzyme. The findings emphasize the importance of an integrated approach to maximize the value of tuna by-products, promoting sustainability in the frame of circular bioeconomy. Overall, these results contribute to the efficient utilization of tuna by-products, waste reduction, and enhance economic viability of the tuna industry.

We investigate \texorpdfstring{$L_2$}{}-approximation problems in the worst case setting in the weighted Hilbert spaces \texorpdfstring{$H(K_{R_{d,\a,\g}})$}{} with weights \texorpdfstring{$R_{d,\a,{\bm \ga}}$}{} under parameters \texorpdfstring{$1\ge \ga_1\ge \ga_2\ge \cdots\ge 0$ and $1<\az_1\le \az_2\le \cdots$}{}. Several interesting weighted Hilbert spaces \texorpdfstring{$H(K_{R_{d,\a,\g}})$}{} appear in this paper. We consider the worst case error of algorithms that use finitely many arbitrary continuous linear functionals. Multivariate approximation; information complexity; tractability; weighted Hilbert spacesWe discuss tractability of \texorpdfstring{$L_2$}{}-approximation problems for the involved Hilbert spaces, which describes how the information complexity depends on \texorpdfstring{$d$}{} and \texorpdfstring{$\va^{-1}$}{}. As a consequence we study the strongly polynomial tractability (SPT), polynomial tractability (PT), weak tractability (WT), and \texorpdfstring{$(t_1,t_2)$}{}-weak tractability (\texorpdfstring{$(t_1,t_2)$}{}-WT) for all \texorpdfstring{$t_1>1$}{} and \texorpdfstring{$t_2>0$}{} in terms of the introduced weights under the absolute error criterion or the normalized error criterion.

In this paper, we study a co-variational inequality problem involving Yosida approximation operators in real uniformly smooth Banach space and define an iterative method to obtain its solution. We prove some properties of Yosida approximation operator for our purpose, that is strongly accretivity and Lipschitz continuity. An existence as well as convergence result is proved for co-variational inequality problem involving Yosida approximation operators using the concept of nonexpansive sunny retraction.

In many Bayesian computations, first, we obtain the expression of the joint distribution of all the unknown variables given the observed data. In general, this expression is not separable in those variables. Thus, obtaining their marginals for each variable and computing the expectations are difficult and costly. This problem becomes even more difficult in high dimensional quandaries, which is an important issue in inverse problems. We may then try to propose a surrogate expression with which we can do approximate computations. Often a separable expression approximation can be useful enough. The Variational Bayesian Approximation (VBA) is a technique that approximates the joint distribution $p$ with an easier, for example separable, one $q$ by minimizing Kullback–Leibler Divergence $KL(q|p)$. When $q$ is separable in all the variables, the approximation is also called Mean Field Approximation (MFA) and so $q$ is the product of the approximated marginals. A first standard and general algorithm is alternate optimization of $KL(q|p)$ with respect to $q_i$. A second general approach is its optimization in the Riemannian manifold. However, in this paper, for practical reasons, we consider the case where $p$ is in the exponential family and so is $q$. For this case, $KL(q|p)$ becomes a function of the parameters $\thetab$ of the exponential family. Then, we can use any other optimization algorithm to obtain those parameters. In this paper, we compare three optimization algorithms: standard alternate optimization, a gradient-based algorithm and a natural gradient algorithm and study their relative performances on three examples.

In this paper, the definition of information entropy of Smoluchowski coagulation equation for Brownian motion is introduced based on coagulation probability. The expression of entropy is the function of geometric average particle volume and standard deviation with lognormal distribution assumption. The asymptotic solution with moment method shows that the entropy is a monotone increasing function of time, which is equivalence to the entropy based on particle size distribution. the result reveals that the present definition of entropy of Smoluchowski coagulation equation are inadequate because the particle average volume at equilibrium cannot be determined from the principle of maximum entropy. This provides a basis for further exploring the global properties of Smoluchowski coagulation equation.

Forest planners have traditionally used expected growth and yield coefficients to predict future merchantable timber volumes. However, because climate change affects forest growth, the typical forest planning methods using expected value of forest growth can lead to sub-optimal harvest decisions. We proposed in this paper to formulate the harvest planning with growth uncertainty due to climate change problem as a multistage stochastic optimization problem and use sample average approximation (SAA) as a tool for finding the best set of forest units that should be harvested in the first period even though we have a limited knowledge of what future climate will be. The objective of the harvest planning model is to maximize the expected value of the net present value (NPV) considering the uncertainty in forest growth and thus in revenues from timber harvest. The proposed model was tested on a small forest with 89 stands and the numerical results showed that the approach allows to have superior solutions in terms of net present value and robustness in face of different climate scenarios compared to the approach using the expected growth and yield. The SAA methods requires to generate samples from the distribution of the random parameter. Our results suggested that a sampling scheme that focuses on generating high number of samples in distant future stages is favorable compared to having large sample sizes for the near future stages. Finally, we demonstrated that, depending on the level of forest growth change, ignoring this uncertainty can negatively affect forest resources sustainability.

In this paper, we study a three step iterative scheme to approximate fixed points of Suzuki's generalized non-expansive mappings. We establish some weak and strong convergence results for such mappings in uniformly convex Banach spaces. Further, we show numerically that iterative scheme (1.8) converges faster than some other known iterations for Suzuki's generalized non-expansive mappings. To support our claim, we give an illustrative example and approximate fixed points of such mappings using Matlab program. Our results are new and generalize several relevant results in the literature.

We present smooth approximations to $ \vert{x} \vert $ using sigmoid functions. In particular $ x\,erf(x/\mu) $ is proved to be better smooth approximation for $ \vert{x} \vert $ than $ x\,tanh(x/\mu) $ and $ \sqrt{x^2 + \mu} $ with respect to accuracy. To accomplish our goal we also provide sharp hyperbolic bounds for error function.

Interactions between mobile robots and human operators in common areas require a high safety especially in terms of trajectory planning, obstacle avoidance and mutual cooperation. In this connection the crossings of planned trajectories, their uncertainty based on model fluctuations, system noise and sensor noise,play an outstanding role. This paper discusses the calculation of expected areas of interactions du ring human-robot navigation with respect to fuzzy and noisy information. Expected crossing points of possible trajectories are nonlinearily associated with positions and orientations of robot and human. The nonlinear transformation of a noisy system input, such as directions of motion of human and robot, to a system output, the expected area of intersection of their trajectories, is done by two methods: statistical linearization and the sigma-point-transformation. For both approaches fuzzy approximations are presented and the inverse problem is discussed where the input distribution parameters are computed from given output distribution parameters.

This paper addresses the evolving landscape of electricity markets in Europe, with a focus on the integration of Renewable Energy Communities as introduced by the Renewable Energy Directive 2018/2001. Residents within a postal code area are highly incentivized to join a community, which enables them to exchange energy among themselves at lower procurement costs. Thereby, energy management systems optimize the operation of respective energy systems, with electrical load forecasting playing a key role. Given that prosumers may switch between communities on a daily basis, electricity demands within these groups will vary, leading to data that is non-stationary, discontinuous as well as non-identical and independently distributed. To encounter this issue, we propose a sophisticated forecasting model that applies federated learning, using informations from various distributed communities to learn domain-invariant features. To achieve this, we initially utilize synthetic electrical load time series at district level and aggregate them to profiles of Renewable Energy Communities with dynamic portfolios. Subsequently, we develop a forecasting model that accounts for the composition of residents of a Renewable Energy Community, adapt data pre-processing in accordance with the time series process, and detail a federated learning algorithm that incorporates weight averaging and data sharing. Following the training of various experimental setups, we ultimately evaluate their effectiveness. The findings suggest that our proposed framework is capable of effectively forecast non-stationary and discontinuous time series and that it can be applied to new, unseen data through the integration of knowledge from multiple sources.

Eastern boundary upwelling systems feature strong zonal gradients of physical and biological ocean properties between cool, productive coastal oceans and warm, oligotrophic subtropical gyres. Zonal currents and jets (striations) are therefore likely to contribute to the transport of water properties between coastal and open oceanic regions. Multi-sensor satellite data are used to characterize the signatures of striations in sea surface temperature (SST), salinity (SSS), and chlorophyll-a (Chl-a) in subtropical eastern North/South Pacific (ENP/ESP) upwelling systems. In the ENP, tracers exhibit striated patterns extending up to ~2500 km offshore. Striations in SST and SSS are highly correlated with quasi-zonal jets, suggesting that these jets contribute to SST/SSS mesoscale patterns via zonal advection. Chl-a striations are collocated with sea surface height (SSH) bands, a possible result of mesoscale eddy trains trapping nutrients and forming striated signals. In the ESP, striations are only found in SST and coincide with SSH bands, consistently with quasi-zonal jets located outside major zonal tracer gradients. An interplay between large-scale SST/SSS advection by the quasi-zonal jets, mesoscale SST/SSS advection by the large-scale meridional flow and eddy advection may explain the persistent ENP hydrographic striations. These results underline the importance of quasi-zonal jets for surface tracer structuring at the mesoscale.

We consider a stationary inclusion in a real Hilbert space X, governed by a set of constraints K, a nonlinear operator A and an element f∈X. Under appropriate assumptions on the data the inclusion has a unique solution, denoted by u. We state and prove a covergence criterion, i.e., we provide necessary and sufficient conditions on a sequence {un}⊂X which guarantee its convergence to the solution u. We then present several applications which provide the continuous dependence of the solution with respect to the data K, A and f, on one hand, and the convergence of an associate penalty problem, on the other hand. We use these abstract results in the study of a frictional contact problem with elastic materials which, in a weak formulation, leads to a stationary inclusion for the deformation field. Finally, we apply the abstract penalty method in the anlysis of two nonlinear elastic constitutive laws.

We shall discuss three methods of inverse Laplace transforms. A Sinc-Thiele approxi- mation, a pure Sinc, and a Sinc-Gaussian based method. The two last Sinc related methods are exact methods of inverse Laplace transforms which allow us a numerical approximation using Sinc methods. The inverse Laplace transform converges exponentially and does not use Bromwich contours for computations. We apply the three methods to Mittag-Leffler functions incorporating one, two, and three parameters. The three parameter Mittag-Leffler function represents Prabhakar’s function. The exact Sinc methods are used to solve fractional differential equations of constant and variable differentiation order.

This work presents a novel approach to construct surrogate models of parametric Differential Algebraic Equations based on a tensor representation of the solutions. The procedure consists in building simultaneously, for every output of the reference model, an approximation given in tensor-train format. A parsimonious exploration of the parameter space coupled with a compact data representation allows to alleviate the curse of dimensionality. The approach is thus appropriate when many parameters with large domains of variation are involved. The numerical results obtained for a nonlinear elasto-viscoplastic constitutive law show that the constructed surrogate model is sufficiently accurate to enable parametric studies such as the calibration of material coefficients.

We propose a new Mamdani fuzzy rule-based system in which the fuzzy sets in the antecedents and consequents are assigned in a discrete set of points and approximated by using the extended inverse fuzzy transforms, whose components are calculated by verifying that the dataset is sufficiently dense with respect to the uniform fuzzy partition. We test our system in the problem of spatial analysis consisting in the evaluation of the liveability of residential housings in all the municipalities of the district of Naples (Italy). Comparisons are done with the results obtained by using trapezoidal fuzzy numbers in the fuzzy rules.

We construct a novel family of summation-integral type hybrid operators in terms of shape parameter $\alpha\in \lbrack 0,1]$ in this paper. Basic estimates, rate of convergence, and order of approximation are also studied using the Korovkin theorem and the modulus of smoothness. We investigate the local approximation findings for these sequences of positive linear operators utilising Peetre's K-functional, Lipschitz class, and second-order modulus of smoothness.

This letter aims to show the connection between the sinc approximation for high-energy absorption cross section and the shadow radius of the spherically symmetric black hole. This connection can give a physical interpretation of the absorption cross section in the eikonal limit parameters. Moreover, the use of this alternative way, one can extract its shadow radius from the absorption cross section in high energy limits to gain more information about the black hole spacetime. Our results indicate that the increasing the value of the shadow radius of the black hole, exponentially increase the the absorption cross section of the black hole in high-energy limits which can be captured by the Event Horizon Telescope (EHT) collaboration.

The SARS coronavirus 2 pandemic affected many areas of public life and industry. This also applies to research particularly that which relies on user test studies. In order to minimize the risk of infection, several aspects of experiment design including the setting might require alteration. In order to develop a step-by-step approach to plan a study with regard to infection protection, an extensive review of the latest research involving the SARS coronavirus 2 pandemic as a blueprint for dealing with other health situations. As a result, a six-step concept was developed that is applicable for user test studies in both stationary rooms and vehicles which can be adapted to the respective circumstances. The infection protection measures determined through research were implemented in the individual sub-steps from study planning to execution. They allow a step-by-step approach to prevent infections in user test studies during a pandemic and in situations where increased hygiene measures are required, in order to continue to carry out user test studies.

In this paper, the existence of two nontrivial stationary solutions for the nonlinear Gilpin Ayala two species competition model is given by using the mountain pass lemma, and the local stability criterion of the trivial solution is given by using Lyapunov function method. Based on the local stability criterion, we give some suggestions on how to avoid the population extinction. This is, when the population is on the verge of extinction, we should try our best to avoid the diffusion behavior and reduce the diffusion coefficient, otherwise the species are easy to go extinct. Numerical example shows the effectiveness of the proposed method.

We investigate the impact of aging on exchangeable inter-arrival times in mixed renewal processes, exploring its implications for reliability and survival analysis. In this study, first, we revisit the definition of renewal point processes, where inter-event time intervals are considered as exchangeable non-negative random variables. Then, we define the concept of statistical aging as latency in the observational process of event counting. Latency affects event detection but preserves exchangeability. However, it may alter the statistical properties of inter-event time intervals. Our analytical and numerical assessments highlight the significance of aging in exchangeable lifetimes, offering insights into key metrics such as the failure survival function, renewal function, and hazard rate function. Through archetypal examples and empirical findings, we illustrate the implications of aging on renewal processes. In particular, employing a Bayesian perspective, we analyze high-frequency currency exchange rate data to assess the impact of aging on volatility risk evaluation. This study contributes novel insights to the literature of renewal theory and survival analysis, emphasizing the role of latency aging in stochastic point processes under exchangeability assumption.

We consider a Cauchy problem for differential equations in a Hilbert space $X$. The problem is stated in a time interval $I$, which can be finite or infinite. Weuse a fixed point argument for history-dependent operators to prove the unique solvability of the problem. Then, we state and prove convergence criteria for both a general fixed point problem and thecorresponding Cauchy problem. These criteria provide necessary and sufficient conditions on a sequence $\{u_n\}$ which guarantee its convergence to the solution of the corresponding problem, in the space of both continuous and continuously differentiable functions. We then specify our results in the study of a particular differential equation governed by two nonlinear operators. Finally, we provide an application in viscoelasticity and give a mechanical interpretation of the corresponding convergence result.

First came the digital banks without offices, and then the “fintech” companies that combined technology and finance to achieve greater efficiency and new business models. Later was the turn of transport and logistics, understood as the sector whose economic activities derived from the transport of people and goods, while on the one hand, it has had a new spring thanks to factors such as online sales. Then, perhaps catalyzed by the pandemic scenario, the turn has reached education, where years ago was only a complement of traditional education, now is a central part with multiple modern methodologies. Numerous studies exist about using or implementing these e-learning procedures, but technical analysis is barely found in references. This work aims to analyze the digital transformation of the main sectors of our society, including finances, transport, and education, together with several examples of how technology was helping to fight the pandemic scenario.

In this work, we consider the properties of the two-term Machin-like formula and develop an algorithm for computing digits of π by using its rational approximation. In this approximation, both terms are constructed by using a representation of 1/π in the binary form. This approach provides the squared convergence in computing digits of π without any trigonometric functions and surd numbers. The Mathematica codes showing some examples are presented.

We study L_2-approximation problems in the weighted Hilbert spaces in the worst case setting. Three interesting weighted Hilbert spaces appear in this paper, whose weights are equipped with two positive parameters $\ga_j$ and $\az_j$ for $j=1,\,2,\dots,\,d$. We consider the worst case error of algorithms that use finitely many arbitrary continuous linear functionals. We discuss the exponential convergence-(t,s)-weak tractability (EC-(t,s)-WT) of these L_2-approximation problems under the absolute or normalized error criterion. In particular, we obtain the sufficient and necessary conditions for EC-(1,1)-WT and EC-(t,1)-WT with t

In this paper we give approximations to the Mittag-Leffler functions in terms of elementary functions using different methods. This allowed us to establish a practical method we called integerization principle. This principle states that many fractional nonlinear oscillators may be solved by means of the solution to some integer-order Duffing oscillator equation. The accuracy of the obtained results is illsutrated in concrete examples. Formulas for estimating the errors in the approximations are also provided.

4-component relativistic atomic and molecular calculations are typically performed within the no-pair approximation where negative-energy solutions are discarded, hence the symmetry between electronic and positronic solutions is not considered. These states are however needed in QED calculations, where furthermore charge conjugation symmetry becomes an issue. In this work we shall discuss the realization of charge conjugation symmetry of the Dirac equation in a central field within the finite basis approximation. Three schemes for basis set construction are considered: restricted, inverse and dual kinetic balance. We find that charge conjugation symmetry can be realized within the restricted and inverse kinetic balance prescriptions, but only with a special form of basis functions that does not obey the right boundary conditions of the radial wavefunctions. The dual kinetic balance prescription is on the other hand compatible with charge conjugation symmetry without restricting the form of the radial basis functions. However, since charge conjugation relates solutions of opposite value of the quantum number κ, this requires the use of basis sets chosen according to total angular momentum j rather than orbital angular momentum ` . As a special case, we consider the free-particle Dirac equation, where the solutions of opposite sign of energy are related by charge conjugation symmetry. We note that there is additional symmetry in those solutions of the same value of κ come in pairs of opposite energy.

The purpose of this paper is to prove strong convergent theorems for Browder's type iterations and Halpern's type iterations of a family of nonexpansive mappings in a complete geodesic space with curvature bounded above by a positive number. Moudafi's viscosity type methods are also discussed without the nice projection property.

This paper deals with bistatic subsurface probing of a horizontally layered dielectric half-space by means of ultra-wideband electromagnetic pulses. A receiver collects reflections from the air-ground interface and from the gradients of dielectric permittivity in the half-space. This scenario is of interest for ground penetrating radar (GPR) applications. For the analytical description of the received signal, we developed and implemented a novel time-domain version of the coupled-wave Wentzel–Kramers–Brillouin approximation. Our solution is in very good agreement with finite-difference time-domain results, radically accelerates calculations, and effectively accounts for the protracted return signals observed in the lower part of the GPR spectrum. The paper includes results showing the application of the proposed technique to two case studies: in particular, the method was employed for the post-processing of experimental radargrams collected on Lake Chebarkul, in Russia, and to simulate GPR probing of the Moon surface, to detect smooth gradients of the dielectric permittivity in lunar regolith.

(1) Background: Considering highly selected patients with ductal carcinoma in situ (DCIS), active surveillance is a valid alternative to surgery. Our study is aimed at showing the reliability of post-biopsy complete lesion removal, documented by mammogram, as additional criterion to select these patients. (2) Methods: 2173 Vacuum Assisted Breast Biopsies (VABB) documented as DCIS have been reviewed. Surgery has been performed in all cases. We retrospectively collected the reports of post-VABB complete lesion removal and the histological results of the biopsy and surgery. We calculated the rate of upgrade of DCIS identified on VABB upon excision for patients with post-biopsy complete lesion removal and for those showing residual lesion. (3) Results: We observed 2173 cases of DCIS: 408 classified as low grade; 1262 as intermediate grade; 503 as high grade. The overall upgrading rate to invasive carcinoma was 15.2% (330/2173). The upgrade rate was significantly lower (8.2%) when considering patients showing mammographically documented complete removal of the lesion. (4) Conclusion: The absence of mammographically documented residual lesion following VABB is associated to a lower upgrading rate of DCIS to invasive carcinoma on surgical excision and should be considered when deciding the proper management DCIS diagnosis.

This article presents a harmonic analysis of the stator currents of a squirrel-cage in-15 duction motor fed by a voltage source inverter with PWM space vector control (SV-PWM). The 16 influence of PWM switching frequency and dead time (dead-band) of controlled transistors on 17 THD and electromagnetic torque ripple is shown. The aim is to determine the lowest switching 18 frequency of the transistors for which the drive will operate correctly. Characteristics were de-19 termined as functions in the form of THD ( ), where the least square approximation was 20 used for stator current measurements when the PWM switching frequency is changed. The ap-21 proximations were realized for simulation and experimental results. To clarify the results, the 22 operation of hardware PWM circuits in microcontrollers was analyzed.

Due to the non-contact measurement characteristics of trackside acoustic technology, it is now utilized for train bearing fault diagnosis. However, the relative motion between the train and the trackside acoustic detection device introduces Doppler aberration in the collected acoustic signal, which affects bearing fault diagnosis. Moreover, when a fault occurs in the train bearing, its acoustic signal exhibits cyclic smoothness characteristics that can be effectively analyzed using the cyclic smoothness method for more accurate judgment. In order to minimize diagnostic errors and enhance accuracy in bearing fault diagnosis, this study integrates bearing fault characteristics with Doppler aberration correction methods and cyclic smoothness techniques for current-stage bearings diagnostics. The overall time-domain graph becomes more compact with an approximately 50% increase in amplitude after correction compared to pre-correction values; other parameters experience enhancements ranging from 20-60%. These results validate the feasibility of our proposed approach and establish a framework for conducting bearing fault diagnosis based on cyclically smoothed Doppler aberration correction.

The water-rich liquid layer immobilized on the surface of the polar stationary phases is critical to the retention of polar compounds in hydrophilic interaction chromatography (HILIC). Although the presence of the adsorbed water layer has been investigated and confirmed by multiple techniques, there is a lack of quantitative measure that can be easily determined and linked to chromatographic parameters. This study proposes a simple measure termed volume ratio (the ratio of the adsorbed water layer volume and the mobile phase volume) that provides a relative, but quantitative information on the adsorbed water layer and may be linked to the phase ratio. The volume ratio can be easily determined using toluene elution volume. The volume ratio values are measured in 25 polar stationary phases in various mobile phase conditions. In addition to the acetonitrile content in the mobile phase, ammonium acetate concentration in the mobile phase and column temperature also have significant influences on the volume ratio and the adsorbed water layer.

Lymphedema is a chronic and debilitating disease that affects up to 250 million patients worldwide. Recent advances in understanding its pathophysiology, along with improved diagnosis and microsurgical techniques, have enhanced our ability to cope with the challenging task of treating this disease. This review provides an overview of the disease from a surgeon's point of view, including existing imaging modalities used for preoperative assessment, as well as surgical procedures used in its treatment. Advantages and drawbacks of various existing modalities used for pre or intraoperative assessment of lymphatic vessels are discussed. Lymphedema treatment has shifted from palliative debulking procedures (liposuction and direct excision) to those aimed at restoring lymphatic flow and countering the pathophysiology of the disease (lymphaticovenous anastomosis and vascularized lymph node transfer). A combination of both approaches can result in a synergistic benefit for patients and are discussed in this review. Despite recent advances, some controversies persist, and further studies are needed to better define surgical treatment algorithms.

As the production of battery cells experiences exponential growth and electric vehicle fleets continue to expand, an escalating number of traction batteries are nearing the conclusion of their operational life for mobility purposes, both presently and in the foreseeable future. Concurrently, the heightened interest in sustainable energy storage solutions has spurred investigations into potential second-life applications for aging traction batteries. Nonetheless, the predominant practice remains the removal of these batteries from electric vehicles, signifying the end of their life cycle, and their subsequent incorporation into recycling processes, with limited consideration for life-extending measures. This study seeks to elucidate the reasons behind the deprioritization of battery repurposing strategies. Therefore, the research team conducted two industry studies with over 20 battery experts from Europe, revealing concerns about the economic viability of repurposing batteries for stationary storage applications. A literature review of studies published since 2016 confirmed the industry's struggles to address this issue theoretically. In conclusion, a research question was formulated, and a solution approach was delineated to assess the economic prospects of aged traction batteries within the industry's landscape in the future. This solution approach encompasses pertinent market analysis, the identification of representative second-life applications, as well as the formulation of a methodology for evaluating the residual value of these batteries.

In this paper, the author utilizes Saddle Theorem and variational methods to deduce existence of at least six stationary solutions for reaction-diffusion Gilpin-Ayala competition model (RDGACM). To obtain the global stabilization of the positive stationary solution of the RDGACM, the author designs a suitable impulsive event triggered mechanism (IETM) to derive the global exponential stability of the the positive stationary solution. It is worth mentioning that the new mechanism can exclude Zeno behavior and effectively reduce the cost of impulse control through event triggering mechanism. Besides, compared with existing literature, the restrictions on the parameters of the RDGACM are relaxed so that the methods used in existing literature can not be applied to the relaxed case of this paper, and so the author makes comprehensive use of Saddle Theorem, orthogonal decomposition of Sobolev space $H_0^1(\Omega)$ and variational methods to overcome the mathematical difficulty. Numerical examples show the effectiveness of the methods proposed in this paper.

Schizoaffective disorder and its classification have always been a topic of discrepancy among researchers. The overlapping presentations of schizoaffective disorder, schizophrenia and psychotic bipolar disorder makes it difficult to classify and diagnose. This study is a narrative review of literatures and genetic and epidemiological research evidences, done to determine the similarities and differences between schizoaffective and psychotic bipolar disorder. Beginning from the introduction of schizoaffective disorder as "schizoaffective psychosis" by Kasanin in 1933, various researchers have proposed different views regarding the diagnosis and classifications for schizoaffective disorder. DSM-III considered schizoaffective disorder as a diagnosis of exclusion as it fails to fit the definite diagnostic criteria of schizophrenia, major affective disorders, or schizophreniform disorder. DSM-V updated the criteria of schizoaffective disorder and stated it as a life time illness rather than being an episodic disorder as in DSM-IV and hence is more reliable. However, some studies show that schizoaffective disorder patients are more like schizophrenia than mood disorder. It still remains unclear whether schizoaffective disorder is a heterogenous disease, a form of schizophrenia, a form of mood disorder or a midpoint in the continuation spectrum of schizophrenia and psychotic bipolar disease.

3D object detection is essential for an accurate and reliable autonomous driving system. Currently, the methods used by the state-of-the-art two-stage detectors are not flexible enough and their fea-ture extraction capabilities are very limited to cope effectively with the disorder and irregularity of point clouds. In this paper, we combine the advantages of both PV-RCNN and PAConv (Position Adaptive Convolution) to create a completely new network, FANet, in order to overcome the ir-regularity and disorder of point clouds. The convolution in our network builds convolutional ker-nels from a basic weight matrix, whose combined coefficients are learned adaptively by LearnNet from relative points. This network allows for flexible modeling of complex spatial variations and geometric structures in the 3D point cloud, enabling better extraction of point cloud features and producing high-quality 3D proposal boxes. Compared to other methods, FANet is superior in terms of 3D object detection accuracy. Extensive experiments on the KITTI dataset have shown a signif-icant improvement in our approach.

In this paper, we present the idea of Self Supervised learning on the Shape Completion and Classification of point clouds. Most 3D shape completion pipelines utilize autoencoders to extract features from point clouds used in downstream tasks such as Classification, Segmentation, Detection, and other related applications. Our idea is to add Contrastive Learning into Auto-Encoders to learn both global and local feature representations of point clouds. We use a combination of Triplet Loss and Chamfer distance to learn global and local feature representations. To evaluate the performance of embeddings for Classification, we utilize the PointNet classifier. We also extend the number of classes to evaluate our model from 4 to 10 to show the generalization ability of learned features. Based on our results, embedding generated from the Contrastive autoencoder enhances Shape Completion and Classification performance from 84.2% to 84.9% of point clouds achieving the state-of-the-art results with 10 classes.

Vienna Atomic Line Database (VALD) contains data on atomic and molecular energy levels and parameters of spectral lines required for stellar spectra analysis. Hundreds of millions lines for fine spectral synthesis and for opacity calculations are collected in present version of VALD (VALD3). Critical evaluation of the data and the diversity of extraction tools support high popularity of VALD among users. The data model of VALD3 incorporates obligatory links to the bibliography making our database more attractive as publishing platform for data producers. The VALD data quality and completeness are constantly improving allowing better reproduction of stellar spectra. To illustrate continuous evolution of the data content we present a comparative analysis of the recent experimental and theoretical atomic data for Fe-group elements, which will be included in the next VALD release. This release will also include a possibility for extracting the line data with full isotopic and hyperfine structures.

In this paper, the optimal approximation algorithm is proposed to simplify non-linear functions and/or discrete data as piecewise polynomials by using the constrained least squares. In time-sensitive applications or in embedded systems with limited resources, the runtime of the approximate function is as crucial as its accuracy. The proposed algorithm search to find the Optimal Piecewise Polynomial (OPP) with minimum computational cost while ensuring the error below a specified threshold. This was accomplished by using smooth piecewise polynomials with optimal order and number of intervals. The computational cost only depends on polynomial complexity, i.e., the order and the number of intervals at runtime function call. For optimal approximation, computational costs for all the possible combinations of piecewise polynomials were calculated and tabulated as ascending order for the specific target CPU off-line. Each combination was optimized through constrained least squares and random selection method for given sample points. Afterward, whether the approximation error is below the predetermined value is examined. When the error is permissible, the combination is selected as the optimal approximation or the next combination was examined. To verify the performance, several representative functions were examined and analyzed.

A hydrophilic silica-based stationary phase with surface bound N-acetylglucosamine (GlcNAc-silica) was prepared in house and characterized physically via Fourier transform infrared (FTIR) and thermogravimetric analysis (TGA) and chromatographically over a wide range of mobile phase compositions. While both FTIR and TGA confirmed the attachment of the GlcNAc ligands to the silica surface, the chromatographic evaluation of the GlcNAc-silica with polar and slightly polar standard solutes (e.g., sugars, nucleic acid fragments, phenolic and benzoic acid derivatives) yielded the typical hydrophilic interaction liquid chromatography (HILIC) behaviors in the sense that retention increased with increased solute’s polarity and the organic content (i.e., acetonitrile) of the hydro-organic mobile phase (i.e., ACN-rich mobile phase). Sugars derivatized with 1-naphthylamine (1-NA) and 2-aminoanthrcene (2-AA) such as xylose, glucose and short chains maltooligosaccharides constituted the most polar species for HILIC retention evaluation, and in addition the maltooligosaccharides offered a polar homologous series for gauging the hydrophilicity of the GlcNAc-silica in analogy with alkylbenzene homologous series and other nonpolar homologous for evaluating the hydrophobicity of non-polar stationary phases. On the other hand, the benzoic acid and phenolic acid derivatives were the probe solutes for evaluating the HILIC retention dependence of ionizable solutes on the pH of the mobile phase. Similarly, the nucleobase and nucleoside weak basic solutes as well as some typical cyclic nucleotide acidic solutes allowed the examination of the dependence of solute retention on the pH of the mobile as well as the polarity of the species.

Recently, we developed Komagataella phaffii (formerly Pichia pastoris) as a model for lipophagy, the selective autophagy of lipid droplets (LDs). We found that lipophagy pathways induced by acute nitrogen (N) starvation and in stationary (S) phase have different molecular mechanisms. Moreover, both types of lipophagy are independent of Atg11, the scaffold protein that interacts with most autophagic receptors and, therefore, is essential for most types of selective autophagy in yeast. Since yeast aggrephagy, the selective autophagy of ubiquitinated protein aggregates, is also independent of Atg11 and utilizes the ubiquitin-binding receptor, Cue5, we studied the relationship of K. phaffii Cue5 with differentially induced LDs and lipophagy. While there was no relationship of Cue5 with LDs and lipophagy under N-starvation conditions, Cue5 accumulated on LDs in S-phase and degraded together with LDs via S-phase lipophagy. The accumulation of Cue5 on LDs and its degradation by S-phase lipophagy strongly depended on the ubiquitin-binding CUE domain and Prl1, the positive regulator of lipophagy 1. However, unlike Prl1, which is required for S-phase lipophagy, Cue5 was dispensable for it suggesting that Cue5 is rather a new substrate of this pathway. We propose that a similar mechanism (Prl1-dependent accumulation on LDs) might be employed by Prl1 to recruit another ubiquitin-binding protein that is essential for S-phase lipophagy.

In this paper, we study a differential operator of parabolic type with a variable and unbounded coefficient, defined on an infinite strip. Sufficient conditions for the existence and compactness of the resolvent are established, and an estimate for the maximum regularity of solutions of the equation Lu=f∈L_2(Ω) is obtained. Two-sided estimates for the distribution function of approximation numbers are obtained. As is known, estimates of approximation numbers show the rate of best approximation of the resolvent of an operator by finite-dimensional operators. The paper proves the assertion about the existence of positive eigenvalues among the eigenvalues of the given operator and finds two-sided estimates for them.

Our goal in this paper is to study the relationship between the linear approximation of Einstein's equations to the Klein-Gordon’s equation. The part one presents what the Klein-Gordon’s equation and the integration of the theory of quantum information in it. The Part two deals with the Stress Energy tensor quantum, wherein the detail I linearized gravity of Einstein equation, and wherein I develop the tensor quantum energy pulse from the equivalence of equation einstein the linearized gravity and the Schrödinger equation relativistic described by Klein-Gordon’s equation.

The purpose of this work is to study quasi-stationary wave structure in the mid-latitude stratosphere and mesosphere (40–50°N) and its role in the formation of the annual ozone cycle. Geopotential height and ozone from Aura MLS data are used and winter climatology for January–February 2011–2020 is considered. More closely examined is the 10-degree longitude segment centered on Longfengshan Brewer station, China, and located in the region of the Aleutian Low influence associated with the quasi-stationary zonal maximum of total ozone. Annual and semi-annual oscillations in ozone were compared using units of ozone volume mixing ratio and concentration, as well as changes in ozone peak altitude and in time series of ozone at individual pressure levels between 316 hPa (9 km) and 0.001 hPa (96 km). The ozone maximum in the vertical profile is higher in volume mixing ratio (VMR) values than in concentration by about 15 km (5 km) in the stratosphere (mesosphere), in consistency with some previous studies. We found that the properties of the annual cycle are better resolved in the altitude range of the main ozone maximum: middle–upper stratosphere in VMR and lower stratosphere in concentration. Both approaches reveal SAO/AO-related changes in the of ozone peak altitudes in a range of 4–6 km during the year. In the lower-stratospheric ozone of the Longfengshan domain, an earlier development of the annual cycle takes place with a maximum in February and a minimum in August compared to spring and autumn, respectively, in zonal means. This is presumably due to the higher rate of dynamical ozone accumulation in the region of the quasi-stationary zonal ozone maximum. The “no-annual-cycle” transition layers are found in the stratosphere and mesosphere. These layers with undisturbed ozone volume mixing ratio throughout the year are of interest for more detailed future study.

The late universe contains a wealth of information about fundamental physics and gravity, wrapped up in non-Gaussian fields. To make use of as much information as possible it is necessary to go beyond two-point statistics. Rather than going to higher order N-point correlation functions, we demonstrate that the probability distribution function (PDF) of spheres in the matter field (a one-point function) already contains a significant amount of this non-Gaussian information. The matter PDF dissects different density environments which are lumped together in two-point statistics, making it particularly useful for probing modifications of gravity or expansion history. Our approach in Cataneo et. al. 2021 extends the success of Large Deviation Theory for predicting the matter PDF in ΛCDM in these “extended” cosmologies. A Fisher forecast demonstrates the information content in the matter PDF via constraints for a Euclid-like survey volume combining the 3D matter PDF with the 3D matter power spectrum. Adding the matter PDF halves the uncertainties on parameters in an evolving dark energy model, relative to the power spectrum alone. Additionally, the matter PDF contains enough non-linear information to substantially increase the detection significance of departures from General Relativity, with improvements up to six times the power spectrum alone. This analysis demonstrates that the matter PDF is a promising non-Gaussian statistic for extracting cosmological information, particularly for beyond ΛCDM models.

Current commitments by European governments seek to improve energy consumption as a means to reduce carbon emissions from building stock by 2050. Within such context, retrieving reliable three-dimensional contours from point clouds becomes an important step in developing facade retrofitting solutions since facade retrofitting projects often make use of as-built 3D models to help reduce inaccuracies by narrowing interpretation and measurement errors. This work aims to provide a method that uses topology-based parametric modelling for reconstructing building envelopes from point clouds. Through a semi-automated process that gives permanent visual feedback, the user adjusts parameters to custom standards of acceptability. A solution under the form of a Grasshopper definition delivers building envelope 3D contours in various file formats as a means for increasing interoperability. The main contributions of this work consist of a parametric reconstruction workflow capable of solving building topology for retrieving 3D contours, a strategy to bypass point cloud occlusion, and a strategy for converting those contours into an IFC model directly from the parametric modelling environment.

In this paper, we present a relapse based demonstrating way to deal with investigate various arrangement MTC information. A commonplace use of this displaying approach incorporates three stages: first, define a model that approximates the connection between quality articulation and trial factors, with boundaries consolidated to address the exploration premium; second, utilize least-squares and assessing condition methods to gauge boundaries and their relating standard blunders; third, register test insights, P-qualities and NFD as proportions of factual criticalness. The benefits of this methodology are as per the following. To begin with, it tends to the exploration interest in a particular, precise way, and maximally uses all the information and other important data. Second, it represents both orderly and irregular varieties related with the information, and the consequences of such examination give not just quality explicit data applicable to the exploration objective, yet additionally its dependability, in this way helping agents to settle on better choices for subsequent investigations. Third, this methodology is truly adaptable, and can undoubtedly be stretched out to different sorts of MTC considers or other microarray explores by detailing various models dependent on the test plan of the investigations.

Extruded polystyrene (XPS) is frequently used in the construction of many different structures. It is therefore necessary to appropriately characterize its mechanical properties to ensure the safety of said structures. Among the available characterization tests, static bending tests are simple and easy to perform; owing to these characteristics, they should be performed more frequently than other tests. However, in static bending tests on XPS, there are several challenges owing to the high flexibility of XPS, and the chosen testing method and sample configuration affect the accuracy of characterization. In this study, three bending properties (Young’s modulus, proportional limit stress, and bending strength) of samples cut from an XPS panel were determined using three-point bending (TPB), four-point bending (FPB), and compression bending (CB) tests with varying sample span/depth ratios, and statistical analyses were performed to determine the relevance of the tests. The experimental results suggest that the TPB and CB tests were more feasible than the FPB test when the span/depth ratio was appropriately determined. However, clear differences were observed in the sample bending properties determined in these tests. In light of these findings, further studies should be conducted to elucidate these differences.

This paper presents the light scattering matrices of atmospheric aggregated hexagonal ice particles appearing in cirrus clouds. In this work aggregates consist of the same particles with different spatial orientation and number of these particles. Two types of particle shape were studied: (1) hexagonal column; (2) hexagonal plate. For both shapes we study compact and non-compact cases of arrangement of particles in aggregates. As a result, four sets of aggregates were made: (1) compact columns; (2) non-compact columns; (3) compact plates; (4) non-compact plates. Each set consists of eight aggregates with different number of particles from 2 to 9. For practical reason the bullet-rosette and the aggregate of hexagonal columns with different sizes was also calculated. The light scattering matrices were calculated for the case of arbitrary spatial orientation within the geometrical optics approximation for sets of compact and non-compact aggregates and within the physical optics approximation for two additional aggregates. It was found that light scattering matrix elements for aggregates are depend on arrangement of particles they are consisted.

In this paper, we introduce a new iteration scheme, named as the S**-iteration scheme, for approximation of fixed point of the nonexpansive mappings. This scheme is faster than Picard, Mann, Ishikawa, Noor, Agarwal, Abbas, Thakur, and Ullah iteration schemes. We show the stability of our instigated scheme and give a numerical example to vindicate our claim. We also put forward some weak and strong convergence theorems for Suzuki's generalized nonexpansive mappings in the setting of uniformly convex Banach spaces. Our results comprehend, improve, and consolidate many results in the existing literature.

A complete MAPLE procedure is designed to implement effectively an algorithm for approximating the trigonometric functions. The algorithm gives a piecewise polynomial approximation on an arbitrary interval, presenting a special partition that we can get its parts, subintervals with ending points of finite rational numbers, together with corresponding approximate polynomials. The procedure takes a sequence of pairs of interval-polynomial as its output that we can easily explore in some useful ways. Examples on calculating approximate values of the sine function with arbitrary accuracy for both of rational and irrational arguments as well as drawing the graph of the piecewise approximate functions will be presented. Moreover, from the approximate integration of integrands of the form $x^m\sin x$ on $[a,b]$, another MAPLE procedure is proposed to find the desired polynomial estimates in norm for the best $L^2$-approximation of the sine function in the vector space $\mathcal{P}_{\ell}$ of polynomials of degree at most $\ell$, a subspace of $L^2(a,b)$.

Coastal cliffs erode in response to short- and long-term environmental changes but predicting these changes continues to be a challenge. In addition to a chronic lack of data on the cliff face, vegetation presence and growth can bias our erosion measurements and limit our ability to detect geomorphic erosion by obscuring the cliff face. This paper builds on past research segmenting vegetation in 3-band red, green, blue (RGB) imagery and presents two approaches to segmenting and filtering vegetation from the bare cliff face in dense point clouds constructed from RGB images and structure-from-motion (SfM) software. Vegetation indices were computed from previously published research and their utility in segmenting vegetation from bare cliff face were compared against machine learning (ML) models for point cloud segmentation. Results demonstrate that, while existing vegetation indices and ML models are both capable of segmenting vegetation and bare cliff face sediments, ML models can be more efficient and robust across different growing seasons. ML model accuracy quickly reached an asymptote with only two layers and RGB images only (i.e., no vegetation indices), suggesting that these more parsimonious models may be more robust to a range of environmental conditions than existing vegetation indices which vary substantially from one growing season to another with changes in vegetation phenology.

This paper introduces a method for tunnel point cloud and BIM model integration and cross-section monitoring, providing information to analyse tunnel cross-sections and surrounding rock deformation, and support for tunnel maintenance and reconstruction. Three types of data are processed for the integration: laser scanning point cloud, BIM tunnel model and terrain model from oblique photogrammetry. An adaptive BIM modelling scheme is proposed for tunnels with alien structures. Precise spatial registration of the data sets is conducted by applying singular value decomposition (SVD) algorithm to calculate transformation parameters from the point cloud model to the BIM model. Since the tunnel central line has high-order derivability, a cross-section calculation method based on tangent vector is proposed to obtain the cross-sectional profile of tunnels at any mileage. The proposed method has been verified by applying it to a tunnel reconstruction project. The experiment results show that the tunnel point cloud and the BIM model were highly coincident after the integration. The developed program can effectively get the cross-section of the tunnel at any mileage, and correctly express the spatial relationship between the BIM tunnel, the point cloud of tunnel and the external mountainous terrain.

This article is devoted to methods of processing random processes. Of particular relevance is the task of processing broadband non-stationary random processes. The processing of random processes is usually related to the assessment of their probabilistic characteristics. Very often, a non-stationary broadband random process is represented by a single implementation in a priori uncertainty about the type of distribution function. Such random processes occur in information and measuring communication systems in which information is transmitted at a real time pace (for example, radio telemetry systems of spacecraft). The use of methods of traditional mathematical statistics, for example, maximum likelihood methods to determine probability characteristics, in this case is not possible. The article discusses a method of processing non-stationary broadband random processes based on the use of non-parametric methods of decision theory. An algorithm for dividing the observation interval into stationary intervals using non-parametric Kendall statistics is considered, as well as methods for estimating probabilistic characteristics on the stationary interval using ordinal statistics. The article presents the results of statistical modeling using the Mathcad program.

The application of transformations of the state equations of continuous linear and bilinear systems to the canonical form of controllability allows one to simplify the computation of Gramians of these systems. In the paper we developed the method and obtain algorithms for computation of the controllability and observability Gramians of continuous linear and bilinear stationary systems with many inputs and one output, based on the method of spectral expansion of the Gramians and the iterative method for computing the bilinear systems Gramians. An important feature of the concept is the idea of separability of the Gramians expansion: sep333arate computation of the scalar and matrix parts of the spectral Gramian expansion reduces the sub-Gramian matrices computation to calculation of numerical sequences of their elements. For the continuous linear systems with one output the method and the algorithm of the spectral decomposition of the controllability Gramian are developed in the form of Xiao matrices. Analytical expressions for the diagonal elements of the Gramian matrices are obtained, making use of which the rest elements can be calculated. For continuous linear systems with many outputs the spectral decompositions of the Gramians in the form of generalized Xiao matrices are obtained, which allows to significantly reduce the number of calculations. The obtained results are generalized for continuous bilinear systems with one output. Iterative spectral algorithms for computation of elements of Gramians of these systems are proposed. Examples are given that illustrate theoretical results.