Domain Of Definition Research Articles

On an Inverse Problem of Identifying an Unknown Boundary for the Biharmonic Equation from Cauchy Data

In this paper, we deal with an inverse problem for the biharmonic equation to find an unknown boundary in the plane by using an additional information assumed on the remaining known part of the boundary. As a by-product, we can uniquely determine the solution everywhere in its domain of definition by supposing that the available data have Fourier expansions. The question of the existence and uniqueness of this inverse problem will be investigated, and we will conclude with some analytical examples to ensure the validity of this study.

Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5th-CASAM-N): I. Mathematical Framework

This work presents the mathematical framework of the “Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5th-CASAM-N),” which generalizes and extends all of the previous works performed to date on this subject. The 5th-CASAM-N enables the exact and efficient computation of all sensitivities, up to and including fifth-order, of model responses to uncertain model parameters and uncertain boundaries of the system’s domain of definition, thus enabling, inter alia, the quantification of uncertainties stemming from manufacturing tolerances. The 5th-CASAM-N provides a fundamental step towards overcoming the curse of dimensionality in sensitivity and uncertainty analysis.

Estimation of compositeness with correction terms

The compositeness X is defined as the probability to observe the composite structure such as the hadronic molecule component in a bound state. One of the model-independent approaches to calculate X is the weak-binding relation. However, when the scattering length a0 is larger than the radius of the bound state R, the central value of the compositeness X becomes larger than unity, which cannot be interpreted as a probability. For the systems with a0 > R, we need to estimate the compositeness with the correction terms. For the reasonable determination of the compositeness, we first present the quantitative estimation of the correction terms. Because the exact value of the compositeness should be contained in its definition domain 0 ≤ X ≤ 1, we propose the reasonable estimation method with the uncertainty band by excluding the region outside of the definition domain of the compositeness. We finally estimate the compositeness of physical systems, and obtain the result which we can interpret as the fraction of the composite component.

Data Model Classification for Interoperability in the Industry

In the context of industry 4.0, interoperability is a major challenge for the manufacturing world. With new use cases heavily depending on industrial data analysis, data structuration through model has become essential for system and process description. However, diversities in data model types due to silo working between domains, represent a challenge for interoperability. Models don't have a clear definition of different domains and there is a need for alignment. This study proposes a classification of different types of data models based on capability criteria to help model definition alignment.

Construction of Autonomous Driving Systems Model Based on the Definition of Operational Design Domain and Proposal of Safety Analysis Approach Based on SOTIF Concept

Construction of Autonomous Driving Systems Model Based on the Definition of Operational Design Domain and Proposal of Safety Analysis Approach Based on SOTIF Concept

Fourier transform method for partial differential equations: Formulas for representing solutions to the Cauchy problem

The paper proposes a method for solving the Cauchy problem for linear partial differential equations with variable coefficients of a special form, allowing, after applying the (inverse) Fourier transform, to rewrite the original problem as a Cauchy problem for first-order partial differential equations. The resulting problem is solved by the method of characteristics and the (direct) Fourier transform is applied to its solution. And for this it is necessary to know the solution of the Cauchy problem for a first-order equation in the entire domain of definition. This leads to the requirement that the support of the (inverse) Fourier transform of the initial function of the original problem be compact, and to describe the class of initial functions, it is necessary to use Paley -Wiener - Schwarz-type theorems on Fourierimages, including distributions. The presentation of solutions in the form of the Fourier transform of some function (distribution), determined by the initial function, is presented. A general form of the evolutionary equation is written down, which, when the described method is applied, leads to the consideration of a homogeneous first-order equation, and a formula for the solution of the Cauchy problem in this general case is derived. The general form of the equation is written down, which leads to the consideration of a first-order inhomogeneous equation, and a formula for solutions it is derived. Particular cases of these equations are the well-known equations that are encountered in the description of various processes in physics, chemistry, and biology.

Image Analysis by Fractional-Order Gaussian-Hermite Moments.

Moments and moment invariants are effective feature descriptors. They have widespread applications in the field of image processing. The recent researches show that fractional-order moments have notable image representation ability. Hermite polynomials are defined over the interval from negative infinity to positive one. Such unboundedness prevents us from developing fractional-order Gaussian-Hermite moments via the existing ideas or approaches. In this paper, we propose fractional-order Gaussian-Hermite moments by forcing the definition domain of Hermite polynomials to be a bounded interval, meanwhile, resorting to a value-decreasing standard deviation to maintain the orthogonality. Moreover, we successfully develop contrast, translation and rotation invariants from the proposed moments based on the inherent properties of Hermite polynomials. The reconstructions of different types of images demonstrate that the proposed moments have more superior image representation ability to the most existing popular orthogonal moments. Besides, the salient performance in invariant image recognition, noise robustness and region-of-interest feature extraction reflect that these moments and their invariants possess the stronger discrimination power and the better noise robustness in comparison with the existing orthogonal moments. Furthermore, both complexity analysis and time consumption indicate that the proposed moments and their invariants are easy to implement, they are suitable for practical engineering applications.

Virtual Validation of an Automated Lane-Keeping System with an Extended Operational Design Domain

Virtual testing using simulation will play a significant role in future safety validation procedures for automated driving systems, as it provides the needed scalability for executing a scenario-based assessment approach. This article combines multiple essential aspects that are necessary for the virtual validation of such systems. First, a general framework that contains the vital subsystems needed for virtual validation is introduced. Secondly, the interfaces between the subsystems are explored. Additionally, the concept of model fidelities is presented and extended towards all relevant subsystems. For an automated lane-keeping system with two different definitions of an operational design domain, all relevant subsystems are defined and integrated into an overall simulation framework. The resulting difference between both operational design domains is the occurrence of lateral manoeuvres, leading to greater demands of the fidelity of the vehicle dynamics model. The simulation results support the initial assumption that by extending the operation domain, the requirements for all subsystems are subject to adaption. As an essential aspect of harmonising virtual validation frameworks, the article identifies four separate layers and their corresponding parameters. In particular, the tool-specific co-simulation capability layer is critical, as it enables model exchange through consistently defined interfaces and reduces the integration effort. The introduction of this layered architecture for virtual validation frameworks enables further cross-domain collaboration.

Analysis on the related factors of China's technological innovation ability using greyness relational degree

PurposeIn order to make grey relational analysis applicable to the interval grey number, this paper discusses the model of grey relational degree of the interval grey number and uses it to analyze the related factors of China's technological innovation ability.Design/methodology/approachFirst, this paper gives the definitions of the lower bound domain, the value domain, the upper bound domain of interval grey number and the generalized measure and the generalized greyness of interval grey number. Then, based on the grey relational theory, this paper proposes the model of greyness relational degree of the interval grey number and analyzes its relationship with the classical grey relational degree. Finally, the model of greyness relational degree is applied to analyze the related factors of China's technological innovation ability.FindingsThe results show that the model of greyness relational degree has strict theoretical basis, convenient calculation and easy programming and can be applied to the grey number sequence, real number sequence and grey number and real number coexisting sequence. The relational order of the four related factors of China's technological innovation ability is research and development (R&D) expenditure, R&D personnel, university student number and public library number, and it is in line with the reality.Practical implicationsThe results show that the sequence values of greyness relational degree have large discreteness, and it is feasible and effective to analyze the related factors of China's technological innovation ability.Originality/valueThe paper succeeds in realizing both the model of greyness relational degree of interval grey number with unvalued information distribution and the order of related factors of China's technological innovation ability.

Comparative analyses of electrical circuits with conventional and revisited definitions of circuit elements: a fractional conformable calculus approach

PurposeThe purpose of this paper is to comparatively analyze the electrical circuits defined with the conventional and revisited time domain circuit element definitions in the context of fractional conformable calculus and to promote the combined usage of conventional definitions, fractional conformable derivative and conformable Laplace transform.Design/methodology/approachThe RL, RC, LC and RLC circuits described by both conventional and revisited time domain circuit element definitions has been analyzed by means of the fractional conformable derivative based differential equations and conformable Laplace transform. The comparison among the obtained results and those based on the methodologies adopted in the previous works has been made.FindingsThe author has found that the conventional definitions-based solution gives a physically reasonable result unlike its revisited definitions-based counterpart and the solutions based on those previous methodologies. A strong agreement to the time domain state space concept-based solution can be observed. The author has also shown that the scalar valued solution can be directly obtained by singularity free conformable Laplace transform-based methodology unlike such state space concept based one.Originality/valueFor the first time, the revisited time domain definitions of resistance and inductance have been proposed and applied together with the revisited definition of capacitance in electrical circuit analyses. The advantage of the combined usage of conventional time definitions, fractional conformable derivative and conformable Laplace transform has been suggested and the impropriety of applying the revisited definitions in circuit analysis has been pointed out.

Collinear factorization of diphoton photoproduction at next to leading order

We calculate in the framework of collinear factorization the amplitude for the photoproduction of a near forward large mass diphoton at leading twist and next to leading order (NLO) in $\alpha_s$. We demonstrate the validity of factorization at this order, which was never achieved for such a reaction where the coefficient function describes a $2 \to 3$ hard process. While the Born order amplitude was purely imaginary and only probed the $x=\pm \xi$ cross-over line of generalized parton distributions (GPD) domain, the NLO result contains both a real and an imaginary part and probes the whole domain of definition of quark GPDs. The phenomenology of our results for medium (JLab) and higher energy (EIC) experiments will be developed in a future study.

Horizontal accuracy assessment of a novel algorithm for approximate a surface to a DEM

Abstract. This study evaluates the horizontal positional accuracy of a new algorithm that defines a surface that approximates DEM data by means of a spline function. This algorithm allows evaluating the surface at any point in its definition domain and allows analytically estimating other parameters of interest, such as slopes, orientations, etc. To evaluate the accuracy achieved with the algorithm, we use a reference DEM 2 m × 2 m (DEMref) from which the derived DEMs are obtained at 4 m × 4 m, 8 m × 8 m and 16 m × 16 m (DEMder). For each DEMder its spline approximant is calculated, which is evaluated at the same points occupied by the DEMref cells, getting a resampled DEM 2 × 2 m (DEMrem). The horizontal accuracy is obtained by computing the area amongs the homologous contour lines derived from DEMref and DEMrem, respectively. It has been observed that the planimetric errors of the proposed algorithm are very small, even in flat areas, where you could expect major differences. Therefore, this algorithm could be used when an evaluation of the horizontal positional accuracy of a DEM product at lower resolution (DEMpro) and a different producing source than the higher resolution DEMref is wanted.

Using multivalued logic for qualitative data analysis

The paper considers a logical approach to data analysis to solve the classification problem. The studied data is a set of objects and their features. As a rule, this is scattered heterogeneous information and it is not enough for a reasonable application of probabilistic models. Therefore, logical algorithms are considered, which under certain conditions may be more adequate. For an expressive formal representation of the relationship between objects and their attributes, multivalued logic is used, and the number of values depends on a specific attribute. Therefore, a system of operations is proposed for variables with different domains of definition. As a result, a decisive function is built, which is a classifier of objects that are present in the studied data. The properties and capabilities of this function are analyzed. It is shown that the logical function, which is a conjunction in the space of rules connecting given objects with their characteristic features, uniquely characterizes the initial data, divides the subject area into classes, possesses modifiability properties, meets the requirements of completeness and consistency in a given area. The paper also proposes an algorithm for its implementation.

Low-Cost Modeling of Microwave Components by Means of Two-Stage Inverse/Forward Surrogates and Domain Confinement

Full-wave electromagnetic (EM) analysis is one of the most important tools in the design of modern microwave components and systems. EM simulation permits reliable evaluation of circuits at the presence of cross-coupling effects or substrate anisotropy, as well as for accounting for interactions with the immediate environment. However, repetitive analyses required by EM-driven procedures, such as parametric optimization or statistical analysis, may entail considerable computational expenditures, often prohibitive. Tackling the high-cost issue fostered the shift toward the incorporation of fast replacement models, including both physics-based surrogates and data-driven ones. While the latter is more popular and versatile, the construction of reliable approximation metamodels for microwave components is hindered by the curse of dimensionality and nonlinearity of system responses. The recent performance-driven modeling methodologies are capable of alleviating these difficulties by confining the surrogate domain to a vicinity of the optimum design manifold (i.e., the region that contains high-quality designs rather than the entire parameter space). Although setting up the model in a constrained domain requires small amounts of training data, domain definition itself requires a set of preoptimized reference designs, acquisition of which is an expensive endeavor. This work proposes a novel approach, which replaces the reference designs with a small set of random observables, thereby considerably reducing the overall cost of the model setup. Comprehensive verification involving several miniaturized microstrip structures demonstrates that our methodology is competitive to performance-driven frameworks both in terms of modeling accuracy and computational efficiency with an average savings of around 80%.

A method of sequentially generating a set of components of a multidimensional random variable using a nonparametric pattern recognition algorithm

We study in which way a priori information on the independence of random variables affects the approximation accuracy of a nonparametric estimate of the Rosenblatt–Parzen probability density. A new technique for generating sets of independent components of a multidimensional random variable is proposed. The methodology is based on testing the hypotheses of the independence of combinations of the multidimensional random variable components using a two-alternative nonparametric kernel algorithm for pattern recognition corresponding to the maximum likelihood criterion. Classes correspond to the domains of definition of the probability densities of sets of independent and dependent components of the multidimensional random variable. Nonparametric statistics of the kernel type are used to estimate the probability densities. The choice of the bandwidths of the kernel estimates of the probability densities is made from the condition of the minimum root-mean-square criterion. The sequential procedure for generating a set of independent components begins with the analysis of paired combinations of components of a multidimensional random variable. For each pair of components, the probability of an error in recognizing classes corresponding to the assumptions of independence and dependence of the considered components is estimated. A pair of components with the maximum difference between these errors is determined. If the errors obtained do not differ significantly, then there are no independent components in the considered multivariate random variable. If there is a significant difference in the probability estimates of class recognition errors, a pair of independent components is established. These components are included in a three-component set of a multidimensional random variable. The analysis of their combinations is carried out in the same way, following the above-described procedure. The process of generating the set of independent components is stopped when no reliable difference occurs any more between the probabilities of errors in recognizing situations belonging to the accepted classes. In this case, the previous set of independent components is the desired result. In contrast to the traditional methodology based on the Pearson criterion, the proposed approach allows us to bypass a problem of the decomposition of the range of values of random variables into multidimensional intervals. The method of generating a set of independent components of a multidimensional random variable is illustrated by the results of the analysis of spectral features of remote sensing data of forest tracts using space imagery from the Landsat-8 satellite.

Dynamics of a Quantum Particle Interacting With an Electromagnetic Field

Essentially, we solve the particle-field equations obtained in the matter distribution quantum mechanics. In the framework of this theory, a particle is described by a density amplitude function, we call wave function, as a packet of waves with the time dependent phases proportional to the relativistic Lagrangian. The mass quantization of such a particle, as a distribution of matter, is obtained from the equality of the spatial integral of the density with the mass as a characteristic of the relativistic dynamics of this matter. The particle dynamics, as a motion of a mass spatial distribution, is obtained from the equality of the wave propagation velocities with the distribution coordinate velocities. This description is a physical one, compared to the Schrödinger-Heisenberg description leading to unphysical results as a null velocity for the kinetic energy as a constant of motion, or Zitterbewegung. The description of a particle interaction with an electromagnetic field by additional Lagrangian terms, with a vector potential conjugated to coordinates, as in the Aharonov-Bohm effect, and an electric potential conjugated to time, leads to the Lorentz force, and the Maxwell equations. In the two conjugated spaces, of the coordinates and of the momentum, the dynamics of a quantum particle is described by propagation operators, depending on the coordinate-momentum product, applied to time dependent wave functions satisfying matter-field equations.  Unlike the standard Schrödinger or Schrödinger-Dirac equations, depending only on the Hamiltonian operator, instead of the Hamiltonian these equations contain the Lagrangian, which, besides the Hamiltonian, include additional terms with an explicit dependence on velocity, as it is expected in a relativistic theory. We obtain the wave function of a particle-antiparticle system interacting with an electromagnetic field, as a wave packet of spinors propagating in space with finite dimensions, given by the finite definition domain of the density function, in the space of the matter-field momentum, as a constant of motion. We show that an electrically charged quantum particle, rotating in a central electric field, generates a vector potential with a magnetic field perpendicular to the rotational plane and an electric field in this plane. By a quantum transition, a photon is emitted in the particle rotational plane, with the magnetic field perpendicular to this plane, and the electric field contained in this plane. In this framework, the vector potential rotation is correlated to a particle momentum rotation, for the canonical matter-field momentum as a constant of motion, without any electromagnetic field radiated outside.

Policy interactions with research trajectories: The case of cyber-physical convergence in manufacturing and industrials

From the early 2010s, policymakers and firms in advanced industrial economies began introducing approaches to systemically exploit manufacturing and industrial data using the notion of cyber-physical convergence. Three innovation concepts have been especially highlighted: Smart Manufacturing, the Industrial Internet and Industrie 4.0. In parallel, academics have employed these concepts in numerous ways to advance their work. Despite this broad interest, precise definition and delineation of the cyber-physical convergence research domain have received little attention. Also missing is systematic knowledge on the interactions of these concepts with research trajectories. This paper fills these gaps by operationalising a newly constructed definition of convergence, and delineating the associated research domain into five data-centric capabilities: Monitoring, Analytics, Modelling and Simulation, Transmission and Security. A bibliometric analysis of the domain is then performed for 2010–2019. There are three findings. First, Analytics and Security have assumed strategic positions within the domain, coinciding with a “strategic turn” in policy. Second, backed by concerted policy and funding efforts, growth in Chinese scientific output has outpaced key competitors, including the U.S. and Germany. Finally, the patterns of promoting their works in terms of the three concepts differ significantly amongst U.S.-, Germany- and China-based authors, which mirrors the different policy discourses prevalent in those countries.

On a Parallelised Diffusion Induced Stochastic Algorithm with Pure Random Search Steps for Global Optimisation

We propose a stochastic algorithm for global optimisation of a regular function, possibly unbounded, defined on a bounded set with regular boundary; a function that attains its extremum in the boundary of its domain of definition. The algorithm is determined by a diffusion process that is associated with the function by means of a strictly elliptic operator that ensures an adequate maximum principle. In order to preclude the algorithm to be trapped in a local extremum, we add a pure random search step to the algorithm. We show that an adequate procedure of parallelisation of the algorithm can increase the rate of convergence, thus superseding the main drawback of the addition of the pure random search step.

Plugin Framework-Based Neuro-Symbolic Grounded Task Planning for Multi-Agent System.

As the roles of robots continue to expand in general, there is an increasing demand for research on automated task planning for a multi-agent system that can independently execute tasks in a wide and dynamic environment. This study introduces a plugin framework in which multiple robots can be involved in task planning in a broad range of areas by combining symbolic and connectionist approaches. The symbolic approach for understanding and learning human knowledge is useful for task planning in a wide and static environment. The network-based connectionist approach has the advantage of being able to respond to an ever-changing dynamic environment. A planning domain definition language-based planning algorithm, which is a symbolic approach, and the cooperative–competitive reinforcement learning algorithm, which is a connectionist approach, were utilized in this study. The proposed architecture is verified through a simulation. It is also verified through an experiment using 10 unmanned surface vehicles that the given tasks were successfully executed in a wide and dynamic environment.

RYR1-related myopathies: Expanding the spectrum of morphological presentation

Mutations in the RYR1 gene are the most common cause of nondystrophic congenital myopathies. Mutations in RYR1 were initially identified in individuals susceptible to malignant hyperthermia, a pharmacogenetic disorder triggered by volatile anesthetics and succinylcholine. Shortly after, mutations in RYR1 were identified in patients with central core disease, which is the most frequent congenital myopathy, and in other muscle disorders, collectively referred to as RYR1-related myopathies. RYR1 mutations are also responsible of some acute pathological conditions triggered by heat- and exercise-induced stress, named exertional heat stroke and exertional-induced rhabdomyolysis, which, similarly to malignant hyperthermia, occur in otherwise healthy individuals with normal skeletal muscle functions. Hundreds of causative mutations linked to RYR1-related diseases have been identified. These mutations are clustered in three regions that are referred to as the N-terminal, central, and C-terminal hot spots. Recent developments in cryo-EM techniques have provided high-resolution reconstructions of the channel, allowing a much better definition of the structural domains within the large N-terminal cytoplasmic region and in the C-terminal domain containing six transmembrane helices and the pore region of the channel. RYR1 mutations may either activate or inhibit channel function or, in some cases, can reduce the expression levels of RYR1 protein. However, similar clinical phenotypes can result from mutations with opposing effects on RYR1 function, or little or no correlation can be found between the observed clinical phenotype and localization of mutations in the structural domains of the RYR1 channel, even though recent studies indicate that clinically severe cases are mostly recessive or due to mutations located in the bridging solenoid. Recent results on the identification of RYR1 mutations in patients with myopathies will be presented.