Search

This paper develops an in-depth treatment concerning the problem of approximating the Gaussian smoothing and the Gaussian derivative computations in scale-space theory for application on discrete data. With close connections to previous axiomatic treatments of continuous and discrete scale-space theory, we consider three main ways of discretizing these scale-space operations in terms of explicit discrete convolutions, based on either (i) sampling the Gaussian kernels and the Gaussian derivative kernels, (ii) locally integrating the Gaussian kernels and the Gaussian derivative kernels over each pixel support region, to aim at suppressing some of the severe artefacts of sampled Gaussian kernels and sampled Gaussian derivatives at very fine scales, or (iii) basing the scale-space analysis on the discrete analogue of the Gaussian kernel, and then computing derivative approximations by applying small-support central difference operators to the spatially smoothed image data. We study the properties of these three main discretization methods both theoretically and experimentally and characterize their performance by quantitative measures, including the results they give rise to with respect to the task of scale selection, investigated for four different use cases, and with emphasis on the behaviour at fine scales. The results show that the sampled Gaussian kernels and the sampled Gaussian derivatives as well as the integrated Gaussian kernels and the integrated Gaussian derivatives perform very poorly at very fine scales. At very fine scales, the discrete analogue of the Gaussian kernel with its corresponding discrete derivative approximations performs substantially better. The sampled Gaussian kernel and the sampled Gaussian derivatives do, on the other hand, lead to numerically very good approximations of the corresponding continuous results, when the scale parameter is sufficiently large, in most of the experiments presented in the paper, when the scale parameter is greater than a value of about 1, in units of the grid spacing. Below a standard deviation of about 0.75, the derivative estimates obtained from convolutions with the sampled Gaussian derivative kernels are, however, not numerically accurate or consistent, while the results obtained from the discrete analogue of the Gaussian kernel, with its associated central difference operators applied to the spatially smoothed image data, are then a much better choice. [ABSTRACT FROM AUTHOR]

The efficiency of controlling the simulated moving bed (SMB) has long been a critical issue in the chemical engineering industry. Most existing research relies on finite element methods, which often result in lower control efficiency and are unable to achieve online control. To enhance control over the SMB process, this paper employs the Crank–Nicolson method to develop a discrete dynamical model. This approach allows for the investigation of system stability and convergence, fundamentally addressing the sources of error. During the discretization of partial differential equations (PDEs), two main types of errors arise: intrinsic errors from the method itself and truncation errors due to derivative approximations and the discretization process. Research indicates that for the former, the iterative process remains convergent as long as the time and spatial steps are sufficiently small. Regarding truncation errors, studies have demonstrated that they exhibit second-order behavior relative to time and spatial steps. The theoretical validation shows that the iteration works effectively, and simulations confirm that the finite difference method is stable and performs well with varying SMB system parameters and controller processes. This provides a solid theoretical foundation for practical, real-time online control. [ABSTRACT FROM AUTHOR]

Macrophages in atherosclerotic lesions exhibit a spectrum of behaviours or phenotypes. The phenotypic distribution of monocyte-derived macrophages (MDMs), its correlation with MDM lipid content, and relation to blood lipoprotein densities are not well understood. Of particular interest is the balance between low density lipoproteins (LDL) and high density lipoproteins (HDL), which carry bad and good cholesterol respectively. To address these issues, we have developed a mathematical model for early atherosclerosis in which the MDM population is structured by phenotype and lipid content. The model admits a simpler, closed subsystem whose analysis shows how lesion composition becomes more pathological as the blood density of LDL increases relative to the HDL capacity. We use asymptotic analysis to derive a power-law relationship between MDM phenotype and lipid content at steady-state. This relationship enables us to understand why, for example, lipid-laden MDMs have a more inflammatory phenotype than lipid-poor MDMs when blood LDL lipid density greatly exceeds HDL capacity. We show further that the MDM phenotype distribution always attains a local maximum, while the lipid content distribution may be unimodal, adopt a quasi-uniform profile or decrease monotonically. Pathological lesions exhibit a local maximum in both the phenotype and lipid content MDM distributions, with the maximum at an inflammatory phenotype and near the lipid content capacity respectively. These results illustrate how macrophage heterogeneity arises in early atherosclerosis and provide a framework for future model validation through comparison with single-cell RNA sequencing data. [ABSTRACT FROM AUTHOR]

The present paper is devoted to the optimisation of parabolic type differential inclusions (DFIs) given by polyhedral set-valued mappings. For this, an auxiliary problem with a polyhedral parabolic discrete inclusion is defined. With the help of locally adjoint mappings and comparison of matrix-coefficients of discrete and discrete-approximate problems, necessary and sufficient optimality conditions for polyhedral-parabolic discrete-approximate inclusions are skilfully constructed. Thus, using the discretisation method and the features of the polyhedral nature of the problem, we prove sufficient optimality conditions for a polyhedral parabolic DFI. At the end of the paper, the numerical results are presented. [ABSTRACT FROM AUTHOR]

The utilization of polymer conformations to construct a variety of superlattices is a common method within the field. However, this technique often results in only long‐range ordering rather than the formation of distinct superlattices. In this study, a well‐organized array of discrete pancake‐shaped superlattices (DPSs) is successfully obtained through the utilization of air–liquid interface self‐assembly, facilitated by the confined environment created by a block copolymer. It is crucial to note that both the self‐assembly behavior and resulting morphologies of the DPSs can be precisely tuned by adjusting several experimental parameters, most notably the concentration and molecular architecture of the block copolymers. Furthermore, this work provides valuable insights into the formation processes and mechanisms underpinning the DPSs. The approach described here is both straightforward and efficacious, establishing a strong foundation for subsequent research and the development of non‐close‐packed superlattice structures. [ABSTRACT FROM AUTHOR]

Myoelectric control, the use of electromyogram (EMG) signals generated during muscle contractions to control a system or device, is a promising input, enabling always-available control for emerging ubiquitous computing applications. However, its widespread use has historically been limited by the need for user-specific machine learning models because of behavioural and physiological differences between users. Leveraging the publicly available 612-user EMG-EPN612 dataset, this work dispels this notion, showing that true zero-shot cross-user myoelectric control is achievable without user-specific training. By taking a discrete approach to classification (i.e., recognizing the entire dynamic gesture as a single event), a classification accuracy of 93.0% for six gestures was achieved on a set of 306 unseen users, showing that big data approaches can enable robust cross-user myoelectric control. By organizing the results into a series of mini-studies, this work provides an in-depth analysis of discrete cross-user models to answer unknown questions and uncover new research directions. In particular, this work explores the number of participants required to build cross-user models, the impact of transfer learning for fine-tuning these models, and the effects of under-represented end-user demographics in the training data, among other issues. Additionally, in order to further evaluate the performance of the developed cross-user models, a completely new dataset was created (using the same recording device) that includes known covariate factors such as cross-day use and limb-position variability. The results show that the large data models can effectively generalize to new datasets and mitigate the impact of common confounding factors that have historically limited the adoption of EMG-based inputs.

The LLC resonant converter has widely been used for having high-frequency soft-switching capability which could lead to high power density power electronic solutions, and higher power conversion efficiency at lower costs. However, the presence of excessive non-linearity resulting from power conversion through the resonant tank has led to a lack of accurate and reliable large-signal and small-signal models which limits the performance optimization. This paper presents a theoretical analysis of the LLC converter using the sampled-data modeling approach to accurately convert the continuous-time-variant state equations to discrete-time-invariant state equations and solve them using switching time-segmented boundary conditions to obtain the discrete large-signal model. The small-signal model is obtained by perturbation and linearization of the steady-state model in the vicinity of the cyclic equilibrium states of the converter. Theoretical analysis results are validated by simulating a 650W LLC converter in Matlab Simulink. Based on the provided results, the proposed steady-state and small-signal models can accurately predict the dynamic behavior of the LLC converter in different operational conditions.

For any two real-valued continuous-path martingales X = {Xt}t≥0 and Y = {Yt}t≥0, with X and Y being orthogonal and Y being differentially subordinate to X, we obtain sharp Lp inequalities for martingales of the form aX + bY with a, b real numbers. The best Lp constant is equal to the norm of the operator aI + bH from Lp to Lp, where H is the Hilbert transform on the circle or real line. The values of these norms were found by Hollenbeck, Kalton and Verbitsky [Studia Math., 2003, 157(3): 237–278]. We also give applications of our martingale inequalities to Riesz transforms and some discrete operators. [ABSTRACT FROM AUTHOR]

This paper presents a comparative study of entropy estimation in a large-alphabet regime. A variety of entropy estimators have been proposed over the years, where each estimator is designed for a different setup with its own strengths and caveats. As a consequence, no estimator is known to be universally better than the others. This work addresses this gap by comparing twenty-one entropy estimators in the studied regime, starting with the simplest plug-in estimator and leading up to the most recent neural network-based and polynomial approximate estimators. Our findings show that the estimators' performance highly depends on the underlying distribution. Specifically, we distinguish between three types of distributions, ranging from uniform to degenerate distributions. For each class of distribution, we recommend the most suitable estimator. Further, we propose a sample-dependent approach, which again considers three classes of distribution, and report the top-performing estimators in each class. This approach provides a data-dependent framework for choosing the desired estimator in practical setups. [ABSTRACT FROM AUTHOR]

The percentage of passing courses is dependent on the assistance provided to students. To ensure the effectiveness of these efforts, identifying students at risk of course failure as early as possible is crucial. The list of students at risk can be generated through academic performance prediction based on historical data. However, the number of students failing (7%) is significantly lower than the number succeeding (93%), resulting in a class imbalance that hampers performance. A widely adopted technique for addressing class imbalance issues is synthetic sample oversampling. Many oversampling techniques neglect discrete features, whereas the existing technique for discrete features treats all features uniformly and does not select samples as a basis for generating synthetic data. This limitation is capable of introducing noise and borderline samples. As a result, this study introduced a novel discrete feature oversampling technique called GLoW SMOTE-D. This technique accelerated the improvement of minority sample learning by performing multiple selections and multiple weighting in order to effectively reduce noise. Experimental results showed that this technique significantly enhanced the performance of students’ failure in the course prediction model when compared to various other techniques across a range of performance measures and classifiers.

The global demand for temporary structures is increasing in the wake of epidemics and wars. The need to build such structures in a prompt, effortless, and inexpensive manner has become a major focus of research. This paper addresses these issues through the use of weaving, an economical and historical construction technique, to achieve the time-cost and economic benefits of temporary construction required in the current environment. Innovative research on unitary and discrete structures was undertaken with the help of computer languages to explore the creation of such discrete structures using two methods: part-to-whole and whole-to-part. Typical design solutions were then selected for physical construction verification and structural optimisation to ensure feasibility and safety. This research attempts to define a complete workflow for this approach, package the relevant knowledge and processes into a digital method, and present them in a practical woven construction in order to fulfil the current demand for the timely and economic construction of temporary buildings.

The efficiency of controlling the simulated moving bed (SMB) has long been a critical issue in the chemical engineering industry. Most existing research relies on finite element methods, which often result in lower control efficiency and are unable to achieve online control. To enhance control over the SMB process, this paper employs the Crank–Nicolson method to develop a discrete dynamical model. This approach allows for the investigation of system stability and convergence, fundamentally addressing the sources of error. During the discretization of partial differential equations (PDEs), two main types of errors arise: intrinsic errors from the method itself and truncation errors due to derivative approximations and the discretization process. Research indicates that for the former, the iterative process remains convergent as long as the time and spatial steps are sufficiently small. Regarding truncation errors, studies have demonstrated that they exhibit second-order behavior relative to time and spatial steps. The theoretical validation shows that the iteration works effectively, and simulations confirm that the finite difference method is stable and performs well with varying SMB system parameters and controller processes. This provides a solid theoretical foundation for practical, real-time online control.

Let \mathbb {G} be a Lie group with solvable connected component and finitely-generated component group and \alpha \in H^2(\mathbb {G},\mathbb {S}^1) a cohomology class. We prove that if (\mathbb {G},\alpha) is of type I then the same holds for the finite central extensions of \mathbb {G}. In particular, finite central extensions of type-I connected solvable Lie groups are again of type I. This is in contrast to the general case, whereby the type-I property does not survive under finite central extensions. We also show that ad-algebraic hulls of connected solvable Lie groups operate on these even when the latter are not simply connected, and give a group-theoretic characterization of the intersection of all Euclidean subgroups of a connected, simply-connected solvable group \mathbb {G} containing a given central subgroup of \mathbb {G}. [ABSTRACT FROM AUTHOR]

Introduction: In musical affect research, there is considerable discussion on the best method to represent affective response. This discussion mainly revolves around the dimensional (valence, tension arousal, energy arousal) and discrete (anger, fear, sadness, happiness, tenderness) models of affect. Here, we compared thesemodels' ability to capture self-reported affect in response to short, affectively ambiguous sounds. Methods: In two online experiments (n1 = 263, n2 = 152), participants rated perceived and induced affect in response to single notes (Exp 1) and chromatic scales (Exp 2), which varied across instrument family and pitch register. Additionally, participants completed questionnaires measuring pre-existing mood, trait empathy, Big-Five personality, musical sophistication, and musical preferences. Results: Rater consistency and agreement were high across all affect scales. Correlation and principal component analyses showed that two dimensions or two affect categories captured most of the variation in affective response. Canonical correlation and regression analyses also showed that energy arousal varied in a manner that was not captured by discrete affect ratings. Furthermore, all sources of individual differences were moderately correlated with all affect scales, particularly pre-existing mood and dimensional affect. Discussion: We conclude that when it comes to single notes and chromatic scales, the dimensions of valence and energy arousal best capture the perceived and induced affective response to affectively ambiguous sounds, although the role of individual differences should also be considered. [ABSTRACT FROM AUTHOR]

Fruit Fly Optimization Algorithm (FOA) is a metaheuristic algorithm inspired by fruit fly foraging behaviours. A large numbers of variants of FOA have been proposed by many researchers. These have been applied to solve various engineering optimization problems. The existing variants and improvements can be categorized as discrete, chaotic, hybrid, improved or modified, and multi-objective. In this paper, a systematic review of FOA has been presented. The review investigates into FOA variants and their pros and cons, as well as FOA applications in various engineering fields. The study is carried out using the PRISMA methodology. The manuscripts have been identified and included in the review using this methodology. In general, researchers around the world confront difficulties in identifying appropriate algorithms to handle real-world optimization problems. This study can be used by researchers to address real-world problems in various domains using FOA, and it can also be used to design variants of FOA and other metaheuristic algorithms. [ABSTRACT FROM AUTHOR]

A new game theoretical approach is proposed to build near-optimal solutions of the social planner in the context of economics. In this regard, one target two-player pursuit-evasion game is designed under complete information where each player's strategy is determined by the dynamics of the optimization problem. The game starts with the move of the evader who aims to follow the optimal policy of the social planner and he is chased by the pursuer whose purpose is to capture his opponent within his target region after a finite number of moves. A novel meta-heuristic approach is developed to design a discrete control model which determines each player's course of action by means of a finite set. Capturing scenarios of the pursuer are provided by designing his finite sets according to the given target range. Numerical experiments are performed in the simple case where the proposed model is compared with grey wolf optimizer through numerical simulations. Here, it is seen that the new model is more effective and accurate which requires less computation and fewer iterations to construct near-optimal solutions. Moreover, the proposed method becomes more powerful for converging to the optimal cost of the problem when the optimal solution is finite. [ABSTRACT FROM AUTHOR]

Background A current argument in the CAM biology literature has focused on the nature of the CAM evolutionary trajectory: whether there is a smooth continuum of phenotypes between plants with C3 and CAM photosynthesis or whether there are discrete steps of phenotypic evolutionary change such as has been modelled for the evolution of C4 photosynthesis. A further implication is that a smooth continuum would increase the evolvability of CAM, whereas discrete changes would make the evolutionary transition from C3 to CAM more difficult. Scope In this essay, I attempt to reconcile these two viewpoints, because I think in many ways this is a false dichotomy that is constraining progress in understanding how both CAM and C4 evolved. In reality, the phenotypic space connecting C3 species and strong CAM/C4 species is both a continuum of variably expressed quantitative traits and yet also contains certain combinations of traits that we are able to identify as discrete, recognizable phenotypes. In this sense, the evolutionary mechanics of CAM origination are no different from those of C4 photosynthesis, nor from the evolution of any other complex trait assemblage. Conclusions To make progress, we must embrace the concept of discrete phenotypic phases of CAM evolution, because their delineation will force us to articulate what aspects of phenotypic variation we think are significant. There are some current phenotypic gaps that are limiting our ability to build a complete CAM evolutionary model: the first is how a rudimentary CAM biochemical cycle becomes established, and the second is how the 'accessory' CAM cycle in C3+CAM plants is recruited into a primary metabolism. The connections to the C3 phenotype we are looking for are potentially found in the behaviour of C3 plants when undergoing physiological stress – behaviour that, strangely enough, remains essentially unexplored in this context. [ABSTRACT FROM AUTHOR]

Water is an integral part of the reproduction of flora and fauna and covers almost 71.4% of the Earth's surface area. It undergoes various chemical, thermal and physical changes due to man-made and natural hazard which deteriorate the quality of water. In order to monitor the quality of water, a consistent monitoring methodology is required. For this reason, Underwater Acoustic Sensor Network (UWASN) came into existence that targets to gather data through the sensors as a wired or wireless network. UWASN is used to capture underwater images for getting information and it indicates that the photographs have valuable evidence for research. However, during transmission, the lifetime of sensor network is rapidly reduced due to limited battery, storage capacity and computational power constraints. Also, the extraction does not provide complete information as the data loss occur due to Doppler spread, path loss and propagation delay, during transmission. Thus, obtaining quality panoramic images using conventional methods, is an eminent challenge due to hostile environment of underwater, that gives rise to issues like poor visibility, distortion, light scattering, noise and wavelength attenuation. Even, the erred pixels and less information in images hinders the analyzing processes used for research, industry and other economic purposes. In order to overcome the limitations, the paper proposes an ensemble technique that refines panoramic images using Mosaicing, Ridgelet and helps to retain the information along with contours by smoothening its edges. It maps line singularities into points via Radon Transform and reconstructs robust periodic images against noise. The proposed solution is validated on underwater images taken from Bubble Vision Dataset. The proposed technique through the computation of Ridglet based Fusion Technique (RBFT), refines panoramic images and combines the pixels of two or more images. The performance of RBFT is measured and compared with state-of-the-art techniques on various parameters like Mean Squared Error (MSE), Peak Signal to Noise Ratio (PSNR), Structural Similarity Index Metrics (SSIM) and Entropy. It is found that RBFT provides approximately 18.5 % less MSE, as an average. This implies that produced images has less erred pixels. As far as PSNR is concerned, RBFT provides high quality resultant panoramic images which is upto an average of 10.8 %. It is observed that RBFT generates approximately 14.3 % higher average SSIM for resultant panoramic images, suggesting that images have higher intensity values. It is found that RBFT provide upto 10.1 % average higher entropy values for resultant panoramic images. It suggests that the images are enriched with content information. Thus, the obtained results support the efficiency of the proposed ensemble technique in terms of quality and visibility of the panoramic images. [ABSTRACT FROM AUTHOR]

The aim of this paper is to describe the use of a discrete, two session large group in an organizational conference setting (of the Faculty of Medical Psychotherapy), which gave insight into unconscious systemic dynamics that affect the organization. In line with a tradition of the use of experiential large group experiences in organizational settings, we illustrate how such a group can be used as a consultative process through bringing forward fresh insights with a compelling emotional intensity and in community building through sharing experiences at a time of stress in mental health services with feelings of increasing isolation. Such insights can aid the organization and its elected officials in leading and developing strategy, whilst community building can lead to collective responsibility-taking and development of collegial relationships which serve to reduce isolation. We clarify different possible functions of the experiential large group in organizational conference settings including consultation regarding systemic dynamics, community building and affective integration of learning. [ABSTRACT FROM AUTHOR]

This paper presents a comparative study of entropy estimation in a large-alphabet regime. A variety of entropy estimators have been proposed over the years, where each estimator is designed for a different setup with its own strengths and caveats. As a consequence, no estimator is known to be universally better than the others. This work addresses this gap by comparing twenty-one entropy estimators in the studied regime, starting with the simplest plug-in estimator and leading up to the most recent neural network-based and polynomial approximate estimators. Our findings show that the estimators’ performance highly depends on the underlying distribution. Specifically, we distinguish between three types of distributions, ranging from uniform to degenerate distributions. For each class of distribution, we recommend the most suitable estimator. Further, we propose a sample-dependent approach, which again considers three classes of distribution, and report the top-performing estimators in each class. This approach provides a data-dependent framework for choosing the desired estimator in practical setups.

The genetic basis of horn fly abundance remains largely unknown and only few heritability estimates are available based on small scale studies. In this study, one subjective and two image-based fly abundance phenotypes were analyzed. Each animal was assessed subjectively for fly abundance by at least one trained agent (SUB). Additionally, several digital images were taken and the best image for each animal was used to assess fly abundance. A box that runs roughly from the withers to the hook and from the chest floor to the fore of the udder was established and all horn flies (PA) and sampling-based estimated number of flies (PR) within the box were calculated. Horn fly counts (SUB, PA, and PR) were discretized into 4 classes based on the quartiles of their respective distributions. Heritability estimates ranged between 0.10 and 0.15 and between 0.14 and 0.16 for the continuous and discrete cases, respectively. The genetic correlation was 0.66 between PA and PR and decreased significantly between the image-based (PA and PR) and the subjective (SUB) assessments for the continuous case. For the discrete case, the genetic correlations between the three traits were very similar, indicating a high concordance between traits.

IntroductionIn musical affect research, there is considerable discussion on the best method to represent affective response. This discussion mainly revolves around the dimensional (valence, tension arousal, energy arousal) and discrete (anger, fear, sadness, happiness, tenderness) models of affect. Here, we compared these models' ability to capture self-reported affect in response to short, affectively ambiguous sounds.MethodsIn two online experiments (n1 = 263, n2 = 152), participants rated perceived and induced affect in response to single notes (Exp 1) and chromatic scales (Exp 2), which varied across instrument family and pitch register. Additionally, participants completed questionnaires measuring pre-existing mood, trait empathy, Big-Five personality, musical sophistication, and musical preferences.ResultsRater consistency and agreement were high across all affect scales. Correlation and principal component analyses showed that two dimensions or two affect categories captured most of the variation in affective response. Canonical correlation and regression analyses also showed that energy arousal varied in a manner that was not captured by discrete affect ratings. Furthermore, all sources of individual differences were moderately correlated with all affect scales, particularly pre-existing mood and dimensional affect.DiscussionWe conclude that when it comes to single notes and chromatic scales, the dimensions of valence and energy arousal best capture the perceived and induced affective response to affectively ambiguous sounds, although the role of individual differences should also be considered.

Brushless DC motor (BLDCM) is a multivariable nonlinear time-varying system, which is difficult to control. The discrete sliding mode control method for BLDCM of electric vehicle on the basis of particle swarm optimization (PSO) is studied to improve the application of BLDCM in electric vehicle. The mathematical model of BLDCM of electric vehicle is established using the state formula. Based on the mathematical model of BLDCM, through the analysis of electromagnetic torque control of BLDCM, it is clear that controlling the angle between rotor flux and stator flux can accurately control the electromagnetic torque of BLDCM. The adaptive discrete sliding mode controller (SMC) is set to control the electromagnetic torque of BLDCM of electric vehicle, and the PSO algorithm is adopted to obtain the optimal parameters of the adaptive discrete SMC to realize the discrete sliding mode control of BLDCM of electric vehicle. According to experimental results, the proposed method can achieve the accurate control of torque and speed of BLDCM of electric vehicle, and increase the application of BLDCM in electric vehicle. [ABSTRACT FROM AUTHOR]

This study aims to describe the various capabilities of the simmer package for R, particularly when running a discrete event simulation model. It then develops a technique for building effective DES simulation models that accurately represent real systems and examines the simulation output on this simmer, both in statistical summary form and parameter estimation. The literature review method with descriptive and exploratory methodologies was employed in this study. When starting with simple models and progressing to more complicated forms step by step while explaining the system with a flow chart, model development is more successful. It is simple to replicate simulations in order to obtain standard error values for model parameter estimators. Creating a discrete event simulation in stages. [ABSTRACT FROM AUTHOR]

The Fuzzy Discrete Mycorrhiza Optimization (FDMOA) Algorithm is a new hybrid optimization method using the Discrete Mycorrhiza Optimization Algorithm (DMOA) in combination with type-1 or interval type-2 fuzzy logic system. In this new research, when using T1FLS, membership functions are defined by type-1 fuzzy sets, which allows for a more flexible and natural representation of uncertain and imprecise data. This approach has been successfully applied to several optimization problems, such as in feature selection, image segmentation, and data clustering. On the other hand, when DMOA is using IT2FLS, membership functions are represented by interval type-2 fuzzy sets, which allows for a more robust and accurate representation of uncertainty. This approach has been shown to handle higher levels of uncertainty and noise in the input data and has been successfully applied to various optimization problems, including control systems, pattern recognition, and decision-making. Both DMOA using T1FLS and DMOA using IT2FLS have shown better performance than the original DMOA algorithm in many applications. The combination of DMOA with fuzzy logic systems provides a powerful and flexible optimization framework that can be adapted to various problem domains. In addition, these techniques have the potential to more efficiently and effectively solve real-world problems. [ABSTRACT FROM AUTHOR]

Statistical tools for data analysis differ for various data types and scales of measurements. The purpose of this review is to discuss these different types of data and measurement scales. To prepare this article, an online literature search was performed in Google and PubMed, using specific keywords. All relevant articles published in the English language between January 2010 and December 2022 were assessed for relevance. Screening of 34 articles was done and eventually 15 were included that had complete information. This review provides detailed information with examples regarding the data types and scales of measurement. Knowledge of the correct data type or scale of measurement is essential for the application of the appropriate statistical tools, and for making accurate inferences.

Let 𝒞ℕ be a monoid which is generated by the partial shift α : n↦n +1 of the set of positive integers ℕ and its inverse partial shift β : n + 1 ↦n. In this paper we prove that if S is a submonoid of the monoid Iℕ∞ of all partial cofinite isometries of positive integers which contains Cscr;ℕ as a submonoid then every Hausdorff locally compact shift-continuous topology on S with adjoined zero is either compact or discrete. Also we show that the similar statement holds for a locally compact semitopological semigroup S with an adjoined compact ideal.

The paper is devoted to the problem of additive fault detection observer design for discrete LTI plants with scalar measurement and external disturbance with the known spectral features. Choice of the observer-filter parameters should maximize its sensitivity to the faults effect and minimize its response to the external disturbance signal. These features are provided by the special filter, generating the corrective signal. The specific spectral approach to discrete H2 optimization in frequency domain, based on the polynomial factorization, is applied with the aim to improve computational effectiveness of the synthesis. Some theoretical aspects are discussed and the novel algorithm of discrete adaptive fault detection observer analytical design is formulated and its effectiveness is demonstrated by the numerical example with implementation of MATLAB package.

The rapid development of technology led to the need to keep pace with it, especially in the field of image processing, because of its importance in the need to get better results. In this paper, new discrete Chebyshev wavelet transforms (DChWT) derived from Chebyshev polynomials (ChP) were proposed and characterized. In terms of orthogonality and approximation (convergence) in the field of mathematics, (ChP) were qualified to transform into discrete wavelets called (DChWT), depending on the mother function with operators (s, r), and were used in image processing to analyze them in the low filter and the high filter so that the image is analyzed into coefficients. Proximity and detail coefficients, which lead to dividing the image into four parts, low left (LL), in which the proximity coefficients are concentrated while the rest of the parts are centered on the detail coefficients, which are high left (HL), low right (LR), and high right (HR), and image compression through the new filter, which has proven its efficiency at level (8) in our results. The results of the proposed wavelets in this work were reached in calculating quality standards in the image obtained after the compression process after comparing them with the results obtained using the standard wavelet used in HaarSymlet 2, Conflict 2, and Daubecheis 2. The most important of these standards is a mean square error (MSE), peak signal-to-noise ratio (PSNR), bit per pixel (BPP), compression ratio (CR), and table one. In this paper, the efficiency of the proposed new wavelets is explained after adding it to MATLAB and according to a specific program to drop in with the basic wavelets to take on their role in important tasks in the image processing area, like artificial intelligence. [ABSTRACT FROM AUTHOR]

The Equilibrium Optimizer (EO) algorithm is a new meta-heuristic algorithm that uses an equilibrium pool and candidates to update particles (solutions). EO algorithm not only has strong exploitation and exploration capabilities but also avoids falling into the local optimum. The reason why EO has these advantages is because of the existence of "generation rate". This paper proposes an Enhanced Equilibrium Optimizer (EEO) Algorithm based on three communication strategies to solve the Job Shop Scheduling Problem (JSSP). To prove the accuracy of the algorithm, this paper uses 28 benchmark functions for testing. At the same time, the Enhanced Equilibrium Optimizer (EEO1, EEO2, EEO3) Algorithms are compared with the existing optimization methods, including Grey Wolf Optimizer (GWO), Multi-Version Optimizer (MVO), Differential Evolution (DE), Whale Optimization Algorithm (WOA). Experiments show that the EO algorithm is significantly better than GWO, MVO, DE, WOA. EO algorithm is mainly used to optimize continuous problems, but JSSP is a discrete application, so the standard equilibrium optimizer algorithm needs to be discretized. This paper extends the enhanced equilibrium optimizer algorithm and adds discretization processing to JSSP. The algorithm is also applied for the job shop scheduling problem by discretization and is compared with the three improvement methods of EEO. Experimental results prove that the algorithm has made significant improvements in solving JSSP. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the dynamics of a discrete commensal symbiosis model with Holling type functional response and density dependent birth rate. Sufficient conditions are obtained for the permanence, partial extinction, and global attractivity of the system. Our analysis presents that the density dependent birth rate plays a crucial role on the dynamic behaviors of the system. Finally, numerical simulations and graphical illustrations are given to indicate the analytical results. [ABSTRACT FROM AUTHOR]

The four most common types of spatial structure (pattern) of landscape cover are identified. The regular nuclear pattern consists of repeating elements, and there is a morphologically distinctive dominant, i.e., a nucleus (one or more). The regular denuclear pattern consists of repeating elements, and the nucleus is not expressed. The irregular nuclear pattern consists of nonrepeating elements, and there is a morphologically distinctive dominant, i.e., a nucleus (one or more). The irregular denuclear pattern consists of nonrepeating elements, and the nucleus is not expressed. Based on spatial features, the most common types of integration and differentiation of landscape cover are identified. The background integration is caused by a single process (a set of processes) that organizes the entire space under consideration and often predetermines the uniformity of the territory. The central integration is caused by the impact of the center on the surroundings and the surroundings on the center. The catenary integration is caused by the middle and far lateral flows of any nature and by the impact on them. The border integration is caused by the connections and interactions of neighboring areas at a common border. The background differentiation is caused by a unified process (a set of processes), which forms heterogeneity due to a different intensity. The central differentiation implies the formation of a center, which plays the role of the leading or dominant element in the functioning and development of the geocomplex/geosystem and is determined by a different nature and a different intensity of its interaction with other elements. The catenary differentiation manifests itself in a directional change in the properties of landscape cover along gradients and is caused by a change in lateral flows. The border differentiation is related to the fact that the boundaries are often a result of a barrier effect of some processes and the reason for the formation of a barrier effect for other processes (synecological, geochemical, geophysical, and geological). The locus differentiation consists of the formation of a separate patch in geocomponents and geocomplex and in the isolation of some part or in the division of the geocomplex into parts. It is emphasized that the selected types of spatial structure, integration, and differentiation are applicable to geocomplexes/geosystems of all levels and to all geocomponents. [ABSTRACT FROM AUTHOR]

The P amplitude value for each cycle has not been carried out even though it is related to indications of atrial hypertrophy. The basic interpretation of the maximum P amplitude under normal conditions is 2.5 small squares on electrocardiogram (ECG) paper which is equivalent to 2.5 mV. Apart from these interpretations, an amplitude value is required that corresponds to the amount of depolarization of the atrial muscle cells. The difficulty faced by researchers is the lack of discrete ecg data available for experiments, so it only depends on amplitude data as a function of Physionet output time. An ECG is produced using discrete data but there is no electrocardiograph that displays discrete data yet. This study aims to obtain the P amplitude value based on discrete electrocardiogram data. The cycle duration value obtained from R to R is used to obtain the initial position of the cycle (sc) with the formula RN+1-1.5dR for each cycle. The P amplitude value can be obtained by filtering the maximum amplitude value between the sc and RN positions. The results of research on 10 physionet samples and 10 RSSA samples showed that all samples had an amplitude R, cycle duration and P amplitude value in each cycle.