Definition Of Function Research Articles

Chattering attenuation analysis in variable structure control for automatic voltage regulator with input constraints

The present paper deals with the chattering attenuation analysis in Variable Structure Control (VSC) for Automatic Voltage Regulators (AVR). As the VSC suffers from the chattering phenomenon, the performances of the soft switching functions are investigated. Signum, saturation, tangent hyperbolic, and fractional approximation functions are used in the proposed controller, and optimum controller parameters are found out separately with Sine Cosine Algorithm. In the definition of the objective function, the overshoot of the step response is restricted by 0.5%. Since every real system has input constraints, the control input and the exciter of the linear AVR model are limited by the direction of IEEE recommendations. It is observed that the calculated control inputs are cropped at the upper and lower limits of the control input. Identical robustness measurements to the previous studies are performed, and the results are compared to each other. While the signum-based switching control exhibits undesirable oscillation, the smooth functions contribute highly acceptable control input. Among the soft switching functions, the tangent hyperbolic and saturation functions are more prominent concerning the disturbance rejection and parameter uncertainties.

On a definition of logarithm of quaternionic functions

For a slice-regular quaternionic function f , the classical exponential function \exp f is not slice-regular in general. An alternative definition of an exponential function, the * -exponential \exp_* , was given in the work by Altavilla and de Fabritiis (2019): if f is a slice-regular function, then \exp_*f is a slice-regular function as well. The study of a * -logarithm \log_*f of a slice-regular function f becomes of great interest for basic reasons, and is performed in this paper. The main result shows that the existence of such a \log_*f depends only on the structure of the zero set of the vectorial part f_v of the slice-regular function f=f_0+f_v , besides the topology of its domain of definition. We also show that, locally, every slice-regular nonvanishing function has a * -logarithm and, at the end, we present an example of a nonvanishing slice-regular function on a ball which does not admit a * -logarithm on that ball.

Convex Programming-Based Robust Optimization Procedure for Blast-Excited Structures with Bounded Uncertainty

Application of the robust optimization (RO) technique to ensure the least possible deviation of structural performance is gaining increasing attention in recent years. However, most RO studies have been conducted in the probabilistic domain, where sufficient uncertainty information is available to construct probability distribution functions of response parameters. But, in many cases, such as for structures under underground blast excitation, hazard parameters like charge weight and charge center distance do not have any definite probability density function. Only their ranges of variations are known to an engineer. Hence, it is more logical to model these parameters as uncertain-but-bounded (UBB) type, which requires only bounds of variations to characterize the uncertainty. The available RO studies in the UBB-domain mainly deal with static loads. Studies on time-variant dynamic loads, such as blast load, are scarce in the existing literature. Also, blast load time-histories show record-to-record variations in their signatures, even with the same setup of hazard parameters. This aspect cannot be considered by the conventional convex programming approaches of RO in the UBB domain. To address all these issues, a new RO procedure is proposed in the present study, which is based on the dual response surface method. The proposed RO procedure can transform the complex simulation-based RO procedure under dynamic blast load to an equivalent deterministic problem with explicit constraints. Thereby, the RO can be easily solved by a gradient-based optimizer. The effectiveness of the proposed approach is elucidated by the complex real-world problems of a multistory building and an underground reinforced concrete bunker. The results are compared with conventional RO approaches. The results show that the proposed approach consistently yields more economic as well as robust solutions in a computationally efficient way.

Advancing functional food regulation

The increasing demand for functional foods, stemming from the growing health consciousness among consumers and their preference for products that provide more than just basic nutrition, presents both opportunities and challenges for regulatory agencies, notably the U.S. Food and Drug Administration (FDA). Functional foods lack a specific regulatory category, leading to uncertainties for manufacturers and consumers. Collaboration between the FDA and the Functional Food Center (FFC) is proposed as a solution to enhance functional food regulation. The FFC's expertise in biomedical sciences and its 17-step process for defining functional foods can contribute valuable scientific research and aid the FDA's evaluation process. By fostering collaboration, both organizations can ensure consumer protection and promote public health while meeting the growing demand for functional foods. Keywords:Functional foods, health claims, regulation, functional food definition, consumer demand, collaboration

An Optimization view on Squash Function of CapsNet

In CapsNet, a bounded measure of the modulus length of the feature is needed, so Squash function is used to compress the feature vector. This paper discusses the definition of Squash function, redefines Squash function based on the idea of information gain rate of decision tree, and constructs CapsNet model on this function. By testing on MNIST, Fashion-MNIST and Cifar-10 datasets, the experimental results show that the Squash function defined in this paper has better classification performance than the traditional Squash function in CapsNet model.

The Maxwell system in nonhomogeneous anisotropic waveguides with slowly stabilizing characteristics of the filling medium

In a domain having several cylindrical outlets to infinity, the stationary Maxwell system with perfectly conductive boundary conditions is studied. The dielectric permittivity and magnetic permeability are assumed to be arbitrary positive definite matrix-valued functions that slowly stabilize at infinity. The authors introduce the scattering matrix, establish the unique solvability of the problem with radiation conditions at infinity, and describe the asymptotics of solutions.

Human-Cyber-Physical Systems for Energy Internet—A Review

As the research of HCPS in EI is ongoing, an increasing number of problems should be addressed, such as the leading role or aid function definition of humans, the coordination of humans with cyber and physical equipment, the state awareness of information handling, etc. Therefore, an increasing number of advanced techniques should be considered and adopted, such as IOT, AI and big data, etc., the main target of which is to improve the timely, digitalized, informationized and intelligent characters of the related tasks. This paper first introduces the applications of CPS in every industry, especially in the power grid and EI (Energy Internet), the introduction of which can be classified as a framework design, support technologies and algorithms, system function, power ancillary service, Energy Internet realization, etc. Then, this paper summarizes the related technologies of Human-Cyber-Physical Systems, which mainly include the areas of system design, theoretical analysis, technique development and application forecasting, which emphasizes its applications in EI. For the development of HCPS, it uses the human-in-the-loop concept and digital transformation as the future research and development directions, the performance of which can be largely promoted through these means. With the aid of HCPS, the optimal system performance of EI can be achieved more robustly, which finally evolves into an integrated and comprehensive modern power grid.

General decay anti-synchronization and [formula omitted] anti-synchronization of coupled reaction-diffusion complex-valued memristive neural networks

This paper studies the general decay anti-synchronization (GDAS) and general decay H∞ anti-synchronization (GDHAS) problems for coupled reaction–diffusion complex-valued memristive neural networks (CRDCVMNNs) without and with time delays. First of all, the concept of GDHAS under the complex-valued case is firstly presented based on the definitions of ψ-type function and ψ-type stability. According to this concept, we further prove a novel lemma which will be used throughout this paper under a new assumption. This lemma is very crucial which gives a new sufficient condition for achieving GDAS of CNNs in complex field. Then, by using the derived lemma and designing a suitable nonlinear feedback controller, some criteria for CRDCVMNNs without and with time delays to realize GDAS and GDHAS are established. At last, two numerical examples are used to verify the effectiveness of the anti-synchronization results.

From complete to selected model spaces in determinant-based multi-reference second-order perturbation treatments.

The present paper reformulates and improves a previously proposed determinant-based second-order multi-reference perturbative formalism. Through a rather simple modification of the energy denominators, this formalism takes into account the interactions between the model space determinants, which are repeated in outer space. The method has been shown to be size-consistent when the model space is a complete active space, which is a severe limit. It is shown here that the completeness of the model space is not necessary to keep this property, provided that the zero-order function satisfies some conditions. For instance, size consistency may be obtained from truncated complete active spaces. It may even be satisfied from Singles and Doubles Configuration Interactions, provided that a coupled electron pair approximation is used in the definition of the model space wave function. The physical content of the method is illustrated by a series of model problems, showing its robustness. A major benefit of the fact that the perturbers are single determinants is the possibility to revise with full flexibility the model-space component of the wave function, i.e., to treat the feedback effect of the dynamic correlation on the valence component of the wave function.

Olfactory dysfunction and its related molecular mechanisms in Parkinson's disease.

Changes in olfactory function are considered to be early biomarkers of Parkinson's disease. Olfactory dysfunction is one of the earliest non-motor features of Parkinson's disease, appearing in about 90% of patients with early-stage Parkinson's disease, and can often predate the diagnosis by years. Therefore, olfactory dysfunction should be considered a reliable marker of the disease. However, the mechanisms responsible for olfactory dysfunction are currently unknown. In this article, we clearly explain the pathology and medical definition of olfactory function as a biomarker for early-stage Parkinson's disease. On the basis of the findings of clinical olfactory function tests and animal model experiments as well as neurotransmitter expression levels, we further characterize the relationship between olfactory dysfunction and neurodegenerative diseases as well as the molecular mechanisms underlying olfactory dysfunction in the pathology of early-stage Parkinson's disease. The findings highlighted in this review suggest that olfactory dysfunction is an important biomarker for preclinical-stage Parkinson's disease. Therefore, therapeutic drugs targeting non-motor symptoms such as olfactory dysfunction in the early stage of Parkinson's disease may prevent or delay dopaminergic neurodegeneration and reduce motor symptoms, highlighting the potential of identifying effective targets for treating Parkinson's disease by inhibiting the deterioration of olfactory dysfunction.

Занятия в вузе: гуманитарный аспект – «сладкий сон» и реальность в повседневной деятельности педагогов высшей школы

The article discusses the author’s forms and methods of work in the course of teaching disciplines of the hu-manities cycle, aimed at activating students in cognition of the studied material, developing their skills in con-ducting scientific discussion. Methodologically, the study is based on empirical work, which involved general scientific methods and techniques (observation, analysis, generalization), as well as special (heuristic, reverse link method, survey, peer-to-peer dialogue). The aim of the study is to represent the general idea of selecting an intensive direction of conducting classes due to the strict time limit. To achieve it a number of tasks were accomplished, including: definition of modern role functionality for teacher and student, characterization of the educational process from the point of view of its restructuring in the direction of cognitive activity activation of students through the introduction of innovative forms and methods of work, identification of key points of the author's methodology of lecture and seminar classes, effectively tested in Kuban universities, recommenda-tions formulation. Conclusion dwells upon the fact that the position of a teacher in higher education should be active, then the solution to the task of improving the quality of education will become real.

Deep Reinforcement Q-Learning for Intelligent Traffic Control in Mass Transit

Traffic control in mass transit consists of the regulation of both vehicle dynamics and passenger flows. While most of the existing approaches focus on the optimization of vehicle dwell time, vehicle time headway, and passenger stocks, we propose in this article an approach which also includes the optimization of the passenger inflows to the platforms. We developed in this work a deep reinforcement Q-learning model for the traffic control in a mass transit line. We first propose a new mathematical traffic model for the train and passengers dynamics. The model combines a discrete-event description of the vehicle dynamics, with a macroscopic model for the passenger flows. We use this new model as the environment of the traffic in mass transit for the reinforcement learning optimization. For this aim, we defined, under the new traffic model, the state variables as well as the control ones, including in particular the number of running vehicles, the vehicle dwell times at stations, and the passenger inflow to platforms. Second, we present our new deep Q-network (DQN) model for the reinforcement learning (RL) with the state representation, action space, and reward function definitions. We also provide the neural network architecture as well as the main hyper-parameters. Finally, we give an evaluation of the model under multiple scenarios. We show in particular the efficiency of the control of the passenger inflows into the platforms.

Demographic, Medical, and Clinical Characteristics of a Population-Based Sample of Patients With Long-lasting Locked-In Syndrome.

Patients with classic locked-in syndrome (LIS), typically caused by ventral pontine stroke, present with quadriplegia, mutism, intact consciousness, and communication skills limited to vertical gazing and/or blinking. Clinical presentations and definitions of LIS differ, especially regarding incomplete LIS. In our study, we explored the functional diversity of LIS, its outcomes, and the complexity of its course along with variations in the location of lesions and their potential significance for outcomes. A national cohort of patients with vascular LIS who remained in the LIS state for at least 6 weeks according to a functional definition of LIS was studied. Demographic, medical, and follow-up data, collected between 2012 and 2022, were obtained from the quality register of the Norwegian National Unit for Rehabilitation of Locked-In Syndrome. Outcomes in verbal communication, motor function, and dependency were evaluated according to criteria for being in or not in the LIS state. The modified Rankin scale and LIS motor recovery scale were applied. Descriptive analysis was performed. The relationship between lesion location and functional outcome was investigated. The sample included 51 patients (median age: 55.7 years, 36 male individuals), 43 of whom had follow-up data. Ischemic stroke was the most common etiology (n = 35). Twenty-three patients had emerged from the LIS state, mostly within 2 years after onset. All but 1 patient achieved some motor improvement, whereas only 3 achieved full motor recovery, and 88% had a persistently high level of dependence. The 3-year survival rate was 87%. Five patients had an isolated pontine lesion, whereas 80% showed various lesions outside the brain stem. Patients who emerged from the LIS state had a significantly lower prevalence of lesions outside the brain stem than patients who remained in the LIS state did. Investigating an unselected population-based sample of patients with vascular LIS offers important insights into the functional diversity of LIS. Although most patients remained severely disabled, even small improvements in function can substantially increase the potential for activity and participation. Additional lesions outside the brain stem seem to be common in long-lasting LIS and might be prognostic for remaining in the LIS state.

Multi-fidelity optimization of metal sheets concerning manufacturability in deep-drawing processes

Multi-fidelity optimization, which complements an expensive high-fidelity function with cheaper low-fidelity functions, has been successfully applied in many fields of structural optimization. In the present work, an exemplary cross-die deep-drawing optimization problem is investigated to compare different objective functions and to assess the performance of a multi-fidelity efficient global optimization technique. To that end, hierarchical kriging is combined with an infill criterion called variable-fidelity expected improvement. Findings depend significantly on the choice of objective function, highlighting the importance of careful consideration when defining an objective function. We show that one function based on the share of bad elements in a forming limit diagram is not well suited to optimize the example problem. In contrast, two other definitions of objective functions, the average sheet thickness reduction and an averaged limit violation in the forming limit diagram, confirm the potential of a multi-fidelity approach. They significantly reduce computational cost at comparable result quality or even improve result quality compared to a single-fidelity optimization.

A high order Cartesian grid, finite volume method for elliptic interface problems

We present a higher-order finite volume method for solving elliptic PDEs with jump conditions on interfaces embedded in a 2D Cartesian grid. Second, fourth, and sixth order accuracy is demonstrated on a variety of tests including problems with high-contrast and spatially varying coefficients, large discontinuities in the source term, and complex interface geometries. We include a generalized truncation error analysis based on cell-centered Taylor series expansions, which then define stencils in terms of local discrete solution data and geometric information. In the process, we develop a simple method based on Green's theorem for computing exact geometric moments directly from an implicit function definition of the embedded interface. This approach produces stencils with a simple bilinear representation, where spatially-varying coefficients and jump conditions can be easily included and finite volume conservation can be enforced.

The deep arbitrary polynomial chaos neural network or how Deep Artificial Neural Networks could benefit from data-driven homogeneous chaos theory

Artificial Intelligence and Machine learning have been widely used in various fields of mathematical computing, physical modeling, computational science, communication science, and stochastic analysis. Approaches based on Deep Artificial Neural Networks (DANN) are very popular in our days. Depending on the learning task, the exact form of DANNs is determined via their multi-layer architecture, activation functions and the so-called loss function. However, for a majority of deep learning approaches based on DANNs, the kernel structure of neural signal processing remains the same, where the node response is encoded as a linear superposition of neural activity, while the non-linearity is triggered by the activation functions. In the current paper, we suggest to analyze the neural signal processing in DANNs from the point of view of homogeneous chaos theory as known from polynomial chaos expansion (PCE). From the PCE perspective, the (linear) response on each node of a DANN could be seen as a 1st degree multi-variate polynomial of single neurons from the previous layer, i.e. linear weighted sum of monomials. From this point of view, the conventional DANN structure relies implicitly (but erroneously) on a Gaussian distribution of neural signals. Additionally, this view revels that by design DANNs do not necessarily fulfill any orthogonality or orthonormality condition for a majority of data-driven applications. Therefore, the prevailing handling of neural signals in DANNs could lead to redundant representation as any neural signal could contain some partial information from other neural signals. To tackle that challenge, we suggest to employ the data-driven generalization of PCE theory known as arbitrary polynomial chaos (aPC) to construct a corresponding multi-variate orthonormal representations on each node of a DANN. Doing so, we generalize the conventional structure of DANNs to Deep arbitrary polynomial chaos neural networks (DaPC NN). They decompose the neural signals that travel through the multi-layer structure by an adaptive construction of data-driven multi-variate orthonormal bases for each layer. Moreover, the introduced DaPC NN provides an opportunity to go beyond the linear weighted superposition of single neurons on each node. Inheriting fundamentals of PCE theory, the DaPC NN offers an additional possibility to account for high-order neural effects reflecting simultaneous interaction in multi-layer networks. Introducing the high-order weighted superposition on each node of the network mitigates the necessity to introduce non-linearity via activation functions and, hence, reduces the room for potential subjectivity in the modeling procedure. Although the current DaPC NN framework has no theoretical restrictions on the use of activation functions. The current paper also summarizes relevant properties of DaPC NNs inherited from aPC as analytical expressions for statistical quantities and sensitivity indexes on each node. We also offer an analytical form of partial derivatives that could be used in various training algorithms. Technically, DaPC NNs require similar training procedures as conventional DANNs, and all trained weights determine automatically the corresponding multi-variate data-driven orthonormal bases for all layers of DaPC NN. The paper makes use of three test cases to illustrate the performance of DaPC NN, comparing it with the performance of the conventional DANN and also with plain aPC expansion. Evidence of convergence over the training data size against validation data sets demonstrates that the DaPC NN outperforms the conventional DANN systematically. Overall, the suggested re-formulation of the kernel network structure in terms of homogeneous chaos theory is not limited to any particular architecture or any particular definition of the loss function. The DaPC NN Matlab Toolbox is available online and users are invited to adopt it for own needs.

Bayesian optimization-assisted approximate Bayesian computation and its application to identifying cyclic constitutive law of structural steels

A costly finite element model discourages Bayesian inference of the underlying parameters from noise-corrupted experimental datasets. This arises because the likelihood of such a model is often computationally intractable, leading to the impossibility of performing a large number of costly simulations. This study presents Bayesian optimization-assisted approximate Bayesian computation (BO-assisted ABC) and showcases its application to identifying the approximate posteriors of parameters for known statistical models and of cyclic elastoplastic parameters for structural steels. ABC bypasses likelihood evaluations by generating prior samples that are assigned as samples constituting the posterior if discrepancies between the experimental dataset and the corresponding simulated datasets do not exceed a small, positive threshold. With a modest number of costly simulations, BO facilitates ABC by intelligently constructing a Gaussian process model that approximates the discrepancy mean function. Identification results from illustrative examples show that the approximate posteriors by the proposed approach not only reproduce a given posterior with acceptable accuracy but also capture the true nominal parameters of a statistical model. Moreover, the approximate posteriors of material parameters can simulate the cyclic elastoplastic behavior of a steel specimen under different loading conditions. The dependence of identification results on definitions of BO acquisition function is also investigated.

Patients with Spinal Muscular Atrophy Type 1 Achieve and Maintain Bulbar Function Following Onasemnogene Abeparvovec Treatment.

Improvement and maintenance of bulbar function are goals of disease-modifying treatments for spinal muscular atrophy (SMA). Lack of standardized measures and a widely accepted definition of bulbar function represents a gap in SMA care. A multidisciplinary team conducted post-hoc analyses of pooled data from one phase 1 (START) and two phase 3 (STR1VE-US, STR1VE-EU) studies to define and evaluate bulbar function of infants with SMA type 1 after receiving one-time gene replacement therapy, onasemnogene abeparvovec. We defined bulbar function as the ability to meet nutritional needs while maintaining airway protection and the ability to communicate verbally. Four endpoints represented adequate bulbar function: (1) absence of clinician-identified physiologic swallowing impairment, (2) receiving full oral nutrition, (3) absence of adverse events indicating pulmonary instability, and (4) the ability to vocalize at least two different, distinct vowel sounds. We descriptively assessed numbers/percentages of patients who achieved each endpoint and all four collectively. Patients were followed until 18 months old (STR1VE-US and STR1VE-EU) or 24 months (START) post-infusion. Overall, 65 patients were analyzed for swallowing, nutrition intake, and adverse events, and 20 were analyzed for communication. At study end, 92% (60/65) of patients had a normal swallow, 75% (49/65) achieved full oral nutrition, 92% (60/65) had no evidence of pulmonary instability, 95% (19/20) met the communication endpoint, and 75% (15/20) achieved all four bulbar function components in the composite endpoint. In these three clinical trials, patients with SMA type 1 who received onasemnogene abeparvovec achieved and maintained the bulbar function criteria utilized within this investigation.

Fuzzy model for assessing the impact of pricing factors on the cost of primary housing

The article presents the results of a study on the creation of a fuzzy model for assessing the impact of pricing factors on the cost of primary real estate. The aim of the study is to develop a fuzzy logic-based tool for analyzing and evaluating the complex relationships between various factors that affect value. The article covers important aspects of creating a fuzzy model, including the definition of pricing factors, linguistic variables, and membership functions. The process of forming a rule base is considered, which determines the logical connections between factors and their influence on the price of real estate. The essence of the concept of primary housing and factors influencing pricing based on data on the situation in the real estate market are considered. The results of the study can be a useful tool for developing pricing strategies and decision making in the real estate market. The model developed by the authors can be improved considering the characteristics of a particular market and available data.

Examination of Zoning Plans on the Basis of Urbanism with an Exponential Function Approach within the Scope of Peer Ratios

After the 1/5000 scale master development plan is created, the relevant local governments create the 1/1000 implementation development plans based on the decision taken by the municipal councils. The aim is to provide the formation of areas that can meet all kinds of needs of the local people. Some islands have different features and notes. One of these featured lots is the zoning islands with only certain precedent values. It has been tried to investigate how and on what basis should be acted while giving building permits to the parcels on these lots with certain precedent values. In the study, it has been shown what should be given a zoning subbase status on these islands, where only the precedent values are given from various plan examples. While these draws are given, it is tried to find the sum of the zoning subbase and total upper areas by considering the definition and value set elements, which are an exponential function definition range, as a method. After the results of giving the zoning diameter on the ground were made in a comparative way against the precedents, how to place the value set on the ground as a subset exponentially from the main plot determined as the domain set was determined by the exponential approach method. The construction in the zoning islands has been made suitable for the building permit, and it has been approached with the exponential function method according to whether the zoning parcels are odd or even number of parcels. In line with the coefficient given by the peers, the approach distances on the ground and the total construction area were tried to be shown with examples.