Arbitrary Form Research Articles

Development of seismic demand prediction models for bridges based on probability approach using symbolic regression method

The resilience assessment of existing structures and designing new resilient ones need to have a precise estimation of seismic responses of the structures traditionally carried out by time-consuming calculations of finite element method. This paper presents interpretable, reliable, and fast prediction models developed by two novel branches of the symbolic regression approach (multigene genetic programming and multi biogeography-based programming) in a probability manner for curved bridges. These newly developed techniques seek to find interpretable equations with arbitrary forms that conform to a specific dataset. The reliable prediction models were developed considering the different uncertainties involved, including mechanical, geometrical, structural, and seismic uncertainties. Due to a large number of input variables for the bridge, the evolutionary correlation coefficient was employed to identify the most influential parameters for seismic demands of bridge components. Parameters with the highest correlation were set as inputs for symbolic regression algorithms, generating closed-form mathematical expressions to predict seismic demands. The resulting explicit models present a fast and accurate model that do not require further simulation or the seismic demand model assumptions to develop bridge fragility curves. In comparison to cloud approach and multiple strips analysis, the new method generates fragility curves with less dispersion.

A POWERFUL SUBVECTOR ANDERSON–RUBIN TEST IN LINEAR INSTRUMENTAL VARIABLES REGRESSION WITH CONDITIONAL HETEROSKEDASTICITY

We introduce a new test for a two-sided hypothesis involving a subset of the structural parameter vector in the linear instrumental variables (IVs) model. Guggenberger, Kleibergen, and Mavroeidis (2019, Quantitative Economics, 10, 487–526; hereafter GKM19) introduce a subvector Anderson–Rubin (AR) test with data-dependent critical values that has asymptotic size equal to nominal size for a parameter space that allows for arbitrary strength or weakness of the IVs and has uniformly nonsmaller power than the projected AR test studied in Guggenberger et al. (2012, Econometrica, 80(6), 2649–2666). However, GKM19 imposes the restrictive assumption of conditional homoskedasticity (CHOM). The main contribution here is to robustify the procedure in GKM19 to arbitrary forms of conditional heteroskedasticity. We first adapt the method in GKM19 to a setup where a certain covariance matrix has an approximate Kronecker product (AKP) structure which nests CHOM. The new test equals this adaptation when the data are consistent with AKP structure as decided by a model selection procedure. Otherwise, the test equals the AR/AR test in Andrews (2017, Identification-Robust Subvector Inference, Cowles Foundation Discussion Papers 3005, Yale University) that is fully robust to conditional heteroskedasticity but less powerful than the adapted method. We show theoretically that the new test has asymptotic size bounded by the nominal size and document improved power relative to the AR/AR test in a wide array of Monte Carlo simulations when the covariance matrix is not too far from AKP.

IMPROVING EFFICIENCY OF SSCA KIDYM DYNAMICS PROGRAM MODULE BY USING AUTOMATICALLY GENERATED DLL-PROCEDURE AND BY OTHER MEANS

The paper presents the results of research on the significant increase in the speed of solving the problems of the dynamics of discrete mechanical systems of an arbitrary form with arbitrary links by a special system of computer algebra (SSCA) KiDyM. In particular, an algorithm for determining the parameters of the additional rotation of the central coordinate systems (CS) of solid bodies in the presence of a non-diagonal inertia tensor to transform them into the main central SCs, in which Euler's equations have the simplest form, is implemented. The main central moments of inertia of the body are determined. A simpler description of SC transformations of robot links with open kinematic chains is proposed. It consists in a separate description of the positions of the SC of the links and the positions of the center of mass and the central SC in relation to the SC of the link. This approach leads to localized description of the kinematics of the mechanism and complete information about the inertial parameters of the link, such as mass, inertia tensor, position of the central SC. The possibility of errors in model descriptions is thereby reduced. On the example of the model of the lower limbs of an human like robot, the gain in the number of machine operations of this description is shown. The use of the software-generated DLL procedure for saving the mathematical model of the system is analyzed in detail. If necessary, it is loaded from an external medium (disk) into the computer's memory during numerical integration. For this purpose, a special procedure has been created in SSCA KiDyM, which transforms the internal representation of analytical expressions of the computer algebra system into program code in C++, calls the appropriate compiler, which creates and saves the DLL-procedure on the disk. In the numerical integration block, the system can load it and calculate the right-hand sides of the Cauchy form of the dynamic equations by the Runge-Kutta procedure. The time gain of this integration method compared to direct calculations of formula trees in PC memory for various tasks is shown. The time gain increases with the increase in the complexity of the mechanical system. A criterion for automatically switching such an algorithm depending on the amount of C++ code in the DLL procedure is proposed.

Analytical and numerical radially symmetric solutions to a heat equation with arbitrary nonlinearity

The paper deals with the construction of radially symmetric heat waves, which are solutions to the heat conduction equation with an arbitrary form of nonlinearity under nonzero boundary condition specified on a moving manifold. The boundary value problem under study is a generalization of those solved by us earlier. Firstly, the class of the considered parabolic equations is extended; secondly, the boundary condition generating a heat wave in a space of arbitrary dimensionality has a more general form. A new theorem of the existence and uniqueness of the heat-wave-type analytical solution is proved for this problem. An approximate method of constructing solutions of the required form is proposed, which is based on expansion in radial basis functions combined with the collocation method. At each time step, the solution is constructed in two stages. The first stage is solving a problem in the region bounded by a specified moving manifold and a heat wave front, which is a priori unknown and evaluated during solving. Herewith, a special substitution is used, i.e. the required function and the spatial variable change their roles. In the second stage, the solution is completed in the region bounded by the positions of the specified moving manifold on a current step and at the initial time. The boundary conditions are defined from the first-step solution. In the test example, the solutions constructed by the developed algorithm are compared with the known exact solution. Calculations show a good accuracy of the numerical solutions at various values of the numerical parameters, including space dimensionality. The observed numerical convergence with respect to the time step shows the correctness of the proposed computational procedure.

A linearization solution for elastic-plastic torsion problems by Edge-based smoothed finite element method

This paper proposes a new scheme for calculating the elastic-plastic uniform torsion of rods considering the hardening behavior of the material. Using PRANDTL-REUSS equation under Hencky proportional loading condition, we develop an elastic-plastic torsion governing equation that can be applied to materials with arbitrary multilinear hardening forms. The edge-based smoothed finite element method is applied to solve the boundary value problem of the above equation. In addition, the incremental scheme is used to calculate the plastic torque. Using the Lagrange interpolation method, the Mises stress is calculated by calculating the gradient in the cell. The nodal stresses are obtained by averaging the stresses at the centroid of the cells. After each load step, the overall domain is divided into elastic and plastic zones according to the yield stresses of the material, and then different governing equations are applied in the different zones. To summarize, this paper provides linearization solutions for nonlinear torsion.

RESOLUTION TIME THEORY IN THE TOPIC OF BROADBAND COMMUNICATIONS. ALGORITHM FOR DATA DEPENDENT JITTER AND CAPACITY ESTIMATIONS WITH POLYNOMIAL TIME EXECUTION

At present, due to the constant growth of the volume of transmitted information, more and more attention is paid to the issues of the possibility of increasing the transmission speed due to the use of the transmission mode "above the Nyquist rate". Despite the relevance of this research topic, due to rather large mathematical difficulties, it is difficult to obtain significant results. One of the theories that allows for a breakthrough is the rapidly developing theory of resolution time developed for phase radio engineering data transmission systems and information measuring optoelectronic systems with PAM-signals with square pulses. This paper presents a novel method for capacity and resolution time estimations with polynomial computational complexity that does not depend on the size of the channel alphabet of PAM-n-signals and is determined only by the effective memory value. The shape of pulse of PAM-n-signals has arbitrary form and amplitudes take only possitive values. The method also allows estimating the time limiting possible deviations due to the sampling error in time, at which the information about the channel symbol will be read error-free or with a given error probability.

On generalized almost para-Hermitian spaces

Recently, a generalized almost Hermitian metric on an almost complex manifold (M, J) is determined as a generalized Riemannian metric (i.e. an arbitrary bilinear form) G which satisfies G(JX, JY) = G(X,Y), where X and Y are arbitrary vector fields on M. In the same manner we can study a generalized almost para-Hermitian metric and determine almost para-Hermitian spaces. Some properties of these spaces and special generalized almost para-Hermitian spaces including generalized para-Hermitian spaces as well as generalized nearly para-K?hler spaces are determined. Finally, a non-trivial example of generalized almost para-Hermitian space is constructed.

PROSPECTIVE DIRECTIONS FOR IMPROVING THE PROCESS OF FORMING THE READINESS OF VOCALIST STUDENTS TO THE STAGE ACTIVITY

The article clarifies the essence of the concept of "readiness of vocal students for stage activities". The need to identify promising directions for improving the process of formation of this phenomenon is substantiated. The dependence of student-vocalists' readiness for stage activities on the quality of preparation of musical works for public interpretation is considered. The spectrum of searches for effective forms and methods of improving the process of formation of the given phenomenon is highlighted thanks to the discovery of promising ideas, the implementation of which makes it possible to achieve perfect readiness of student vocalists for stage activities. The organization and course of a research experiment aimed at testing the effectiveness of well-founded hypotheses regarding the expedient use of voluntary and involuntary types of memory of student vocalists in the process of preparing a concert program for a stage presentation is described. It has been experimentally proven that effective forms and methods of improving the process of purposeful formation of students-vocalists' readiness for stage activities are those that enable them to use an arbitrary form of memorizing musical and literary text, and during its reproduction (creative interpretation) - a mixed one.Key words: readiness of vocal students for stage activities, musical works, forms and methods of memorizing sheet music, voluntary memory, involuntary memory.

Performance Stability of a Pianist and the Specificity of its Formation in the Preparation Process to Concert and Stage Activities

The performance stability of a pianist is characterized as not innate, but an acquired integraldynamic property, the manifestation of which ensures the preservation of optimal emotional and creative well-being in the conditions of concert and stage activity, aimed at a clear representation of the artistic images of musical works and their expressive implementation by means of error-free reproduction of performance skills. The role of the pianist's performance stability in the mental creation of a model of a musical piece, the basis of which is artistic images built by the transformation of perceived musical material into sound constructs with their imaginary emotional and timbral coloring, and in the mental creation of a program of technical and tactical actions, thanks to which the defined images are realized, is clarified. It was established that the performance stability of a pianist can be formed both purposefully (arbitrarily) and spontaneously (involuntarily) in the process of preparation for concert and stage activities. The specifics of the formation of the performance stability of a pianist in the process of preparation for concert and stage activities are considered. It has been proven that the voluntary (purposeful) form of formation of the performance stability of the pianist is more effective than the involuntary (spontaneous) form. Emphasis is placed on the expediency of using an arbitrary (targeted) form of formation of the given phenomenon, as it enables the pianist to create in his imagination artistic images of a musical piece and a program of technical and tactical actions with conscious introduction of the necessary corrections to their structural and functional components during preparation for a concert and stage interpretation. It was found that the involuntarily (spontaneously) formed performance stability of a pianist is much more difficult to be consciously corrected with the aim of its positivization. The stages of the arbitrary form of formation of the pianist's performance stability are described in accordance with the functional orientation of the essential features of the phenomenon in the process of his preparation for concert and stage activities.

Response of nonlinear oscillators with fractional derivative elements under evolutionary stochastic excitations: A Path Integral approach based on Laplace’s method of integration

In this paper, an approximate analytical technique is developed for determining the non-stationary response amplitude probability density function (PDF) of nonlinear/hysteretic oscillators endowed with fractional element and subjected to evolutionary excitations. This is achieved by a novel formulation of the Path Integral (PI) approach. Specifically, a stochastic averaging/linearization treatment of the original fractional order governing equation of motion yields a first-order stochastic differential equation (SDE) for the oscillator response amplitude. Associated with this first-order SDE is the Chapman–Kolmogorov (CK) equation governing the evolution in time of the non-stationary response amplitude PDF. Next, the PI technique is employed, which is based on a discretized version of the CK equation solved in short time steps. This is done relying on the Laplace’s method of integration which yields an approximate analytical solution of the integral involved in the CK equation. In this manner, the repetitive integrations generally required in the classical numerical implementation of the procedure are avoided. Thus, the non-stationary response amplitude PDF is approximately determined in closed-form in a computationally efficient manner. Notably, the technique can also account for arbitrary excitation evolutionary power spectrum forms, even of the non-separable kind. Applications to oscillators with Van der Pol and Duffing type nonlinear restoring force models, and Preisach hysteretic models, are presented. Appropriate comparisons with Monte Carlo simulation data are shown, demonstrating the efficiency and accuracy of the proposed approach.

A finite strain model for multi-material, multi-component biomechanical analysis with total Lagrangian smoothed finite element method

In this paper, a Unified-Implementation of smoothed finite element method (UI-SFEM) is presented for analyzing large deformations of complex biological tissues using automatically generated linear triangles and tetrahedrons. Biological structures, including many multi-material, multi-component connected tissues, usually undergo finite deformation. Numerical method need to consider different numerical difficulties for different component or materials. In our method, the numerical integration domain can be constructed by combining arbitrary forms of smoothing domains based on gradient smoothing techniques according to the numerical characteristics of materials or components. In addition, the instantaneous hyperelasticity and time-dependent viscous behaviors commonly in biological tissues are considered. Numerical experiments, including fiber reinforced biological composites, the artery wall and cervical spine, show that the UI-SFEM possesses the following properties in simulating multi-material and multi-component biological tissues: (1) remarkably flexibility (2) high accuracy and computational efficiency. (3) insensitive to mesh distortion.

Mapping renormalized coupled cluster methods to quantum computers through a compact unitary representation of nonunitary operators

Nonunitary theories are commonly seen in the classical simulations of quantum systems. Among these theories, the method of moments of coupled cluster equations (MMCCs) and the ensuing classes of the renormalized coupled cluster (CC) approaches have evolved into one of the most accurate approaches to describe correlation effects in various quantum systems. The MMCC formalism provides an effective way for correcting the energies of approximate CC formulations (parent theories) using moments, or CC equations, that are not used to determine approximate cluster amplitudes. In this paper, we propose a quantum algorithm for computing MMCC ground-state energies that provides two main advantages over classical computing or other quantum algorithms: (i) the possibility of forming superpositions of CC moments of arbitrary ranks in the entire Hilbert space and using an arbitrary form of the parent cluster operator for MMCC expansion, and (ii) significant reduction in the number of measurements in quantum simulation through a compact unitary representation for a generally nonunitary operator. We illustrate the robustness of our approach over a broad class of test cases, including $\ensuremath{\sim}40$ molecular systems with varying basis sets encoded using 4--40 qubits, and we exhibit the detailed MMCC analysis for the 8-qubit half-filled, four-site, single impurity Anderson model and the 12-qubit hydrogen fluoride molecular system from the corresponding noise-free and noisy MMCC quantum computations. We also outline the extension of the MMCC formalism to the case of a unitary CC wave-function Ansatz.

Targeting resources efficiently and justifiably by combining causal machine learning and theory.

Efficient allocation of limited resources relies on accurate estimates of potential incremental benefits for each candidate. These heterogeneous treatment effects (HTE) can be estimated with properly specified theory-driven models and observational data that contain all confounders. Using causal machine learning to estimate HTE from big data offers higher benefits with limited resources by identifying additional heterogeneity dimensions and fitting arbitrary functional forms and interactions, but decisions based on black-box models are not justifiable. Our solution is designed to increase resource allocation efficiency, enhance the understanding of the treatment effects, and increase the acceptance of the resulting decisions with a rationale that is in line with existing theory. The case study identifies the right individuals to incentivize for increasing their physical activity to maximize the population's health benefits due to reduced diabetes and heart disease prevalence. We leverage large-scale data from multi-wave nationally representative health surveys and theory from the published global meta-analysis results. We train causal machine learning ensembles, extract the heterogeneity dimensions of the treatment effect, sign, and monotonicity of its moderators with explainable AI, and incorporate them into the theory-driven model with our generalized linear model with the qualitative constraint (GLM_QC) method. The results show that the proposed methodology improves the expected health benefits for diabetes by 11% and for heart disease by 9% compared to the traditional approach of using the model specification from the literature and estimating the model with large-scale data. Qualitative constraints not only prevent counter-intuitive effects but also improve achieved benefits by regularizing the model.

Dynamic analysis of coupled piezoelectric motivator system with flexible connections

This study comprehensively analyzes the dynamic responses for sandwich coupled piezoelectric motivator system (CPMS) with flexible connections including couplings and supports. The excitation equations are derived independently to obtain the external rotor loads of various forms such as moving concentrated or moving distributed loads. Based on the coordinates transformation and wave numbers recombination, a solution for the coupling of multi-segment structures in arbitrary form is given by using the method of reverberation-ray matrix (MRRM). The novel feature of this approach lies in that the piezoelectric vibrator of straight-straight, straight-curved coupling under moving load with arbitrary patterns can be solved uniformly, and the connection stiffness at each node can be controlled by the virtual springs. Afterwards, a detailed visualization and parametric discussion are performed to investigate the dynamic transverse displacements, which shows that the loading velocity and width can significantly affect the dynamic characteristics of CPMS within a certain range, and the vibration responses between the unloaded and loaded sections are related. Furthermore, the geometric parameters and thermoelectric effects also play significant roles on the dynamic responses in corresponding load velocity range.

Guarantees in case of deprivation of property under the law of the European Convention on Human Rights

From the content of the property right, the guarantees of protection against arbitrary or disproportionate forms of interference in the exercise of this fundamental right of the person result. Such interference may take the form of deprivation or limitation of rights. Every individual has the right to own property and to use the goods in his possession. Depriving the person of his property can only take place in the case of the existence of a public necessity. If these circumstances occur, the state is obliged to ensure fair compensation. Both governments and others are prohibited from assigning property without justification. In this article, we propose to analyze the relevant provisions of the European Convention on Human Rights, as well as the general principles established by the European Court of Human Rights in cases where deprivation of property is invoked.

Spherically symmetric wormholes in minimally coupled f(R,T) gravity

In this manuscript, we construct a spherical thin shell wormhole in the background of the minimally coupled f(R, T) model. In this gravitational theory, f is an arbitrary functional form that depends on the Ricci scalar (R) as well as the trace of stress-energy tensor (T). To continue our systematic analysis, we use a cut and paste approach to link two surfaces, i.e., interior and exterior. We find energy-momentum density along with surface pressure for f(R, T) gravitational f(R, T) = R + α R 2 + λ T model, by using the Lanczos equation. We utilize the polytropic equation of state to check the dynamical behavior of the wormhole. A standard potential approach is applied to check the stability of constructed wormhole with throat radius a 0. Graphical analysis shows that the stability regions of wormholes rely on the specific values mass M to charge Q ratio.

The Role of EU Legal Regulation in the Responsibility of Private Business for the Implementation of Sustainable Development Concepts

The study considers the mechanism of legal regulation of the practical implementation of sustainable development by private business. The main periods of implementation of this mechanism are determined and it is indicated that the practical implementation began in 2015-2017. The implementation trends were quite peaceful, without administrative pressure and legal abuses. Despite numerous scientific studies of this scientific problem, it should be noted that the implementation of EU legal requirements by international companies outside the EU legal area has not been sufficiently studied. Therefore, the purpose of the study was to assess the EU legal requirements in the development of sustainable development through the information content of financial and non-financial reporting of TNCs operating in Ukraine. The analysis of compliance with the conditions for the implementation of Directive 2014/95/EU in Ukraine is carried out. It is established that in the modern period the concept of sustainable development is realized by the management of private business structures. They realize that it is necessary to disseminate and convey information about the activities of enterprises to a wide range of society. It is noted that according to Directive 2014/95/EU, business structures do not submit financial statements in an arbitrary form, but the practice has developed three forms: Sustainability report (SR), Integrated report (IR), Corporate Social Responsibility (CSR) report. The evolution of changes in the approach to non-financial reporting is traced.

Impact of the Dropping Function on Clustering of Packet Losses.

The dropping function mechanism is known to improve the performance of TCP/IP networks by reducing queueing delays and desynchronizing flows. In this paper, we study yet another positive effect caused by this mechanism, i.e., the reduction in the clustering of packet losses, measured by the burst ratio. The main contribution consists of two new formulas for the burst ratio in systems with and without the dropping function, respectively. These formulas enable the easy calculation of the burst ratio for a general, non-Poisson traffic, and for an arbitrary form of the dropping function. Having the formulas, we provide several numerical examples that demonstrate their usability. In particular, we test the effect of the dropping function’s shape on the burst ratio. Several shapes of the dropping function proposed in the literature are compared in this context. We also demonstrate, how the optimal shape can be found in a parameter-depended class of functions. Finally, we investigate the impact of different system parameters on the burst ratio, including the load of the system and the variance of the service time. The most important conclusion drawn from these examples is that it is not only the dropping function that reduces the burst ratio by far; simultaneously, the more variable the traffic, the more beneficial the application of the dropping function.

Semi-analytical solutions of static and dynamic degenerate, nondegenerate and functionally graded electro-elastic multilayered plates

In this paper mathematical modelling and semi-analytical solutions are elaborated based on the extended Stroh-like formalism for 3-D static problems of electro-elastic mono and multilayered plates. For the dynamic analysis of such structures under various excitation types, a time trigonometric series was coupled with the Stroh-like formalism. The unknown coefficient vectors are solution of the resulted eigenvalue problems and the solution is obtained in the associated basis. Mechanical and electrical forces are applied on the top and/or bottom layer and may take arbitrary forms. A flexible matrix formulation is elaborated to easily account for arbitrary mechanical and electrical surface loads and excitations. The methodological approach focuses on various aspects including the electro-elastic effects, the degeneracy of elastic isotropic materials as well as the effect of the graded material’s factor. Analytical solutions are obtained for the static behavior of degenerate and non-degenerate Elastic FGM plates, where the eigenvalues and eigenvectors are explicitly given. Mainly, semi-analytical solutions are presented for the dynamic behavior of piezoelectric sandwich plates by coupling Stroh-like formalism and trigonometric series. The presented methodological approach is applied to the dynamical analysis of sandwich plates under various excitation forms, namely sinusoidal, rectangular and sawtooth excitation pulses. The obtained numerical results demonstrate the effect of the graded factor, degeneracy and the applied surface load as well as of the excitation on mechanical and electrical responses for various laminated plates.

Pushforwards via scattering equations with applications to positive geometries

In this paper we explore and expand the connection between two modern descriptions of scattering amplitudes, the CHY formalism and the framework of positive geometries, facilitated by the scattering equations. For theories in the CHY family whose S-matrix is captured by some positive geometry in the kinematic space, the corresponding canonical form can be obtained as the pushforward via the scattering equations of the canonical form of a positive geometry defined in the CHY moduli space. In order to compute these canonical forms in kinematic spaces, we study the general problem of pushing forward arbitrary rational differential forms via the scattering equations. We develop three methods which achieve this without ever needing to explicitly solve any scattering equations. Our results use techniques from computational algebraic geometry, including companion matrices and the global duality of residues, and they extend the application of similar results for rational functions to rational differential forms.