Real Functions Research Articles

Size and Depth of Monotone Neural Networks: Interpolation and Approximation.

We study monotone neural networks with threshold gates where all the weights (other than the biases) are nonnegative. We focus on the expressive power and efficiency of the representation of such networks. Our first result establishes that every monotone function over [0,1]d can be approximated within arbitrarily small additive error by a depth-4 monotone network. When , we improve upon the previous best-known construction, which has a depth of d+1 . Our proof goes by solving the monotone interpolation problem for monotone datasets using a depth-4 monotone threshold network. In our second main result, we compare size bounds between monotone and arbitrary neural networks with threshold gates. We find that there are monotone real functions that can be computed efficiently by networks with no restriction on the gates, whereas monotone networks approximating these functions need exponential size in the dimension.

Construction and realization of simulation training environment based on AI-assisted simulation of real scenarios of dispatching and commanding operations

Abstract Dispatch command business is an essential and important part of modern society's production and life. With the development of science and technology, the use of AI-assisted construction of simulation training environments is of enormous significance to the development and improvement of the dispatching command business. The study facilitates the acquisition and preprocessing of data from the three-dimensional scene used in the scheduling command simulation training, refines the details of the simulation environment using a multi-resolution hierarchical detail model, and enables the creation of a simulation training environment for the scheduling command using three-dimensional modeling and optimization technology. In this paper, the dispatching system trained in a simulation environment is better than other dispatching systems in terms of dispatching accuracy, starting difficulty, and feedback effectiveness. The satisfaction rate for scheduling demand on different subway lines is significantly better than other scheduling algorithms. As the sampling area expands, the FID and NRMSE values of the generated real map decrease, but the PSNR and NRMSE values increase. This paper generates a dispatching command simulation training environment with a fidelity level of “excellent” and a simulation quality that exhibits a high degree of realism and credibility.

The Relationship between Energy Inflation and Exchange Rate: A Study on Türkiye

Energy is among the indicators that are taken into consideration in increasing the production levels of countries and increasing their welfare. Energy has become an indispensable resource for the industrialization of countries, increasing their industrial production and ensuring their development and growth in this direction. Today, the development and growth of countries have become linked to their energy consumption. However, countries that lack energy resources need to import the energy resources they need in order to realize their development and growth, and their economic activities for this purpose are closely related to other economic indicators, especially the exchange rate, and bring about a series of economic results. This study examines the existence of the relationship between energy inflation and the real exchange rate in Türkiye in light of the fact that Türkiye is heavily dependent on foreign energy consumption. Accordingly, the study utilizes monthly series of energy inflation and real exchange rate variables for the period 2012:M01-2021:M12 for Türkiye. In the study, firstly, the series of the variables are seasonally adjusted with the help of a computer package program, then the variables are logarithmically transformed and the stationarity of the series of the variables is analyzed. According to the results of ADF and PP unit root tests, it is concluded that the series of energy inflation and real exchange rate variables are not stationary at level, but both series become stationary after first differences are taken. In the study, Engle-Granger cointegration analysis was conducted in accordance with the unit root test results. According to the results of cointegration analysis, energy inflation and real exchange rate variables are found to move together in the long run. Finally, Granger causality test analysis was conducted and according to the results of this analysis, the existence of bidirectional causality in the Granger sense between energy inflation and real exchange rate was determined.

PENGARUH TINGKAT PENGANGGURAN TERBUKA DAN INFLASI TERHADAP PDRB RIIL TAHUN 2002–2022 KOTA MEDAN

The purpose of this research is the influence of inflation and open unemployment rate on the growth of Real GRDP of Medan City. The sample used is the data of inflation variable and open unemployment rate variable and Real GRDP growth variable of Medan City from 2007 to 2022. The results of the study obtained that the inflation variable has no significant effect on the growth of Real GRDP of Medan City, the open unemployment rate variable has no significant effect on the growth of Real GRDP of Medan City, together the inflation variable and the open unemployment rate have no significant effect on the growth of Real GRDP of Medan City. and the influence of the inflation variable and the open unemployment rate variable on the growth of Real GRDP is 3.5%, the remaining 96.5% is explained by other variables or factors not discussed in this study.

Fuzzy Moderation and Moderated-Mediation Analysis of Real Estate Variables in South Korea

Fuzzy Moderation and Moderated-Mediation Analysis of Real Estate Variables in South Korea

An application of Hayashi's inequality in numerical integration

Abstract This study systematically develops error estimates tailored to a specific set of general quadrature rules that exclusively incorporate first derivatives. Moreover, it introduces refined versions of select generalized Ostrowski’s type inequalities, enhancing their applicability. Through the skillful application of Hayashi’s celebrated inequality to specific functions, the provided proofs underpin these advancements. Notably, this approach extends its utility to approximate integrals of real functions with bounded first derivatives. Remarkably, it employs Newton-Cotes and Gauss-Legendre quadrature rules, bypassing the need for stringent requirements on higher-order derivatives.

On Logarithmic Holder Condition and Local Extrema of Power Takagi Functions

This paper studies one class of real functions, which we call Takagi power functions. Such functions have one positive real parameter; they are continuous, but nowhere differentiable, and are given on a real line using functional series. These series are similar to the series defining the continuous, nowhere differentiable Takagi function described in 1903. For each parameter value, we derive a functional equation for functions related to Takagi power functions. Then, using this equation, we obtain an accurate two-sides estimate for the functions under study. Next, we prove that for parameter values not exceeding 1, Takagi power functions satisfy the Holder logarithmic condition, and find the smallest value of the constant in this condition. As a result, we get the usual Hölder condition, which follows from the logarithmic Hölder condition. Moreover, for parameter values ranging from 0 to 1, we investigate the behavior of Takagi power functions in the neighborhood of their global maximum points. Then we show that the functions under study reach a strict local minimum on the real axis at binary-rational points, and only at them. Finally, we describe the set of points at which our functions reach a strict local maximum. The benefit of our research lies in the development of methods applicable to continuous functions that cannot be differentiated anywhere. This can significantly expand the set of functions being studied.

Adaptive smoothing of retinotopic maps based on Teichmüller parametrization

Retinotopic mapping, the mapping between visual inputs on the retina and neural responses on the cortical surface, is one of the fundamental topics in visual neuroscience. In human studies, retinotopic maps are conventionally constructed and processed by decoding blood oxygenation-level dependent (BOLD) functional magnetic resonance imaging (fMRI) responses to designed visual stimuli on the cortical surface. However, these methods frequently generate retinotopic maps that do not preserve topology, contradicting a fundamental property of retinotopic maps observed in neurophysiology. To address this problem, we propose an integrated approach to simultaneously refine the flattening from the 3D cortical surface to the 2D parametric space and adaptively smooth retinotopic perception centers in the visual space to make the retinotopic maps topological. One key element of the approach is the enhanced error tolerant Teichmüller mapping, which refines the parametrization by minimizing angle distortions and maximizing alignment to noisy landmarks. We validated our overall approach with synthetic and real retinotopic mapping datasets and applied it to compute cortical magnification factor (CMF). The results showed that the proposed approach was superior to other conventional retinotopic mapping methods in predicting BOLD fMRI time series and preserving topology.

Chaotic neural networks with complex-valued weight and its applications in electrocardiogram classification

As neural networks are easy to converge to local minimum, the ergodicity of chaotic system is helpful to tackle this problem. Besides, the real parts and imaginary parts in complex-valued chaotic systems are independent, which increase the ergodic property and unpredictability of the chaotic signals. Therefore, we propose a new chaotic neural network with complex-valued weight for electrocardiogram classification. Firstly, a complex Logistic chaotic map is put forward, and its bifurcation diagram, Lyapunov index, and chaotic attractors are analyzed. Secondly, based on the ergodicity of complex Logistic chaotic map and a novel neuron function, the learning algorithm including complex-valued weight iteration for the chaotic neural network is proposed. Finally, the MIT-BIH data-base is used to verify the proposed method. The chaotic neural network with real Logistic map and other classification methods are also adopted for comparison. The results show that our chaotic neural network has a certain improvement in the accuracy of electrocardiogram classification.

Effect of Economic Policy Uncertainty on Exchange Rate Volatility in Pakistan

This study examines the effect of economic policy uncertainty on Pakistan’s exchange rate. Pakistan’s exchange rate always remains under pressure due to the widening inflow-outflow gap in foreign exchange. The volatile exchange rates make it harder for businesses to invest and make inflation more uncertain, which ultimately slows down productivity and GDP growth. Due to the close linkages of the exchange rate with the economic indicators, it is required to examine the effect of different economic variables on the exchange rate and its volatility by incorporating the role of economic policy uncertainty. The study uses the sample of Jan 2011 to Dec 2022 for the empirical results. The study employs the EGARCH model for empirical results. The aftermaths of the mean equation of the EGARCH model suggest that economic policy uncertainty has a positive effect on Pakistan’s exchange rate. Moreover, an increase in the economic policy uncertainty scale, increases the volatility in Pakistan’s exchange rate. The primary source of exchange rate volatility is the nominal variable rather than the real variables. On the basis of the study’s findings, certain relevant recommendations were given in order to stabilize the foreign exchange market in Pakistan.

Identification of Control Parameters Using Taguchi Method for Hybrid Real-Binary Differential Evolution Algorithm and Its Applications in Electromagnetic Optimization

The hybrid real-binary differential evolution (HDE) algorithm has been proficient in addressing electromagnetic optimization problems (EOPs) involving both real and binary variables. However, its optimization performance on different control parameter (CP) settings is not further studied, and the method to determine the values of CPs is more likely to use the trial-and-error method, which lacks universality on both unimodal and multimodal benchmarks. To completely account for the effect of CPs in HDE, the Taguchi method is utilized to identify the values of each CP. The orthogonal experiment result is the average rank of the mean values of 23 benchmark functions obtained by HDE and other classic optimization algorithms. Based on the analysis of variance results, three CPs that have a major effect on the performance of HDE are selected, and each of them is changed from level 1 to level 5 to further obtain the best combination of CPs, which is indicated as HDEN1. To further enhance the local search ability of HDEN1 for the global best, a modified algorithm (HDEN2) is proposed based on a novel mutation strategy selection method, and the simulation results demonstrate that the minimum values obtained by HDEN2 are smaller than those obtained by HDEN1. Two EOPs, including planar microwave absorber and Yagi-Uda antenna designs, are solved to validate the performance of HDEN1 and HDEN2. The results reveal that the HDEN1 and HDEN2 outperform HDE, demonstrating the efficacy of the proposed method for identifying the CPs of HDE. In the end, a low profile and wideband RCS reduction pixelated checkboard metasurface is optimized utilizing the HDEN2, proving that the proposed algorithm can be a good candidate for hybrid real-binary electromagnetic problems.

More is less - Adding zoom levels in multi-scale maps to reduce the need for zooming interactions

When you zoom in or out of current multi-scale cartographic applications, it is common to feel lost and disoriented for a few seconds because dimensions and map symbols have changed. To make the exploration of these multi-scale maps more fluid, one option is to design maps where the transformations due to scale change are more progressive. This paper proposes to use cartographic generalization techniques to design these multi-scale maps with additional intermediate scales to improve progressiveness. These more progressive maps are tested in a user study with a task requiring multiple zooms in and out. The users perform better with the progressive maps, and in particular, the total quantity of required zooming is reduced compared to maps without additional intermediate scales. However, the survey is not fully conclusive on task performance due to the complexity of such a survey with real maps. This difficulty in assessing how well progressive map generalisation reduces disorientation is discussed and guidelines are proposed to design further studies.

Robust job shop scheduling with machine unavailability due to random breakdowns and condition-based maintenance

This paper presents a novel solution approach for a variant of the job shop scheduling problem with machine unavailability due to both condition-based preventive maintenance and corrective maintenance following random breakdowns. We first provide an exact mathematical formulation of the problem under simplifying assumptions, namely that the number of breakdowns for each job position on each machine is known, the degradation rates are fixed, and the preventive and corrective maintenance durations are deterministic parameters. Moreover, to handle the more realistic case of stochastic machine degradation, random breakdowns, and uncertain maintenance durations, a simulation-optimisation algorithm is proposed. The real makespan function is first approximated using multiple surrogate measures, which are optimised through independent genetic algorithms. Then, the fittest solutions obtained from these surrogate measures are simulated, and the best among them is added to an elite list, which is included in the genetic algorithms' populations for the next iteration. Schedule robustness is ensured by using an objective function that consists of the weighted average of the expected makespan and its 90th percentile. Furthermore, to reduce the likelihood of falling into a local optimum, a stopping criterion based on simulated annealing is implemented. Numerical experimentation on extended benchmark instances confirmed the validity of the mathematical formulation and the favourable performance of the proposed simulation-optimisation algorithm in terms of computational time and solution quality.

Efficient and Parallel Implementation of Real and Complex Response Functions Employing the Second-Order Algebraic-Diagrammatic Construction Scheme for the Polarization Propagator.

We present the implementation of an efficient matrix-folded formalism for the evaluation of complex response functions and the calculation of transition properties at the level of the second-order algebraic-diagrammatic construction (ADC(2)) scheme. The underlying algorithms, in combination with the adopted hybrid MPI/OpenMP parallelization strategy, enabled calculations of the UV/vis spectra of a guanine oligomer series ranging up to 1032 contracted basis functions, thereby utilizing vast computational resources from up to 32,768 CPU cores. Further analysis of the convergence behavior of the involved iterative subspace algorithms revealed the superiority of a frequency-separated treatment of response equations even for a large spectral window, including 101 frequencies. We demonstrate the applicability to general quantum mechanical operators by the first reported electronic circular dichroism spectrum calculated with a complex polarization propagator approach at the ADC(2) level of theory.

On the problem of a Gurtin–Murdoch cylindrical material surface embedded in an infinite matrix

The problem of an infinite isotropic elastic matrix subjected to uniform far-field load and containing a Gurtin–Murdoch material surface of cylindrical shape is considered in plane strain setting. The governing equations and the boundary conditions for the problem, reduced to that of an infinite plane containing a material curve along a circular arc, are reviewed. The displacements inside the matrix are sought in the complex variables form of a single layer elastic potential whose density represents the jump in complex tractions across the curve. Exact complex integral representations for the elastic fields everywhere in the material are provided and the problem is further reduced to the system of real variables hypersingular boundary integral equations in terms of the strain and rotation components associated with the curve. The components are then approximated by the series of trigonometric functions that are multiplied by the square root weight functions to allow for automatic incorporation of the tip conditions. The unknown coefficients in the series are found from the system of linear algebraic equations that is solved using standard collocation method. The numerical examples are presented to illustrate the influence of dimensionless parameters with the main focus on the study of curvature-induced effects.

Zadacha Koshi dlya nagruzhennogo uravneniya Kortevega–de Friza v klasse periodicheskikh funktsiy

The inverse spectral problem method is applied to finding a solution of the Cauchyproblem for the loaded Korteweg–de Vries equation in the class of periodic infinite-gap functions.A simple algorithm for constructing a high-order Korteweg–de Vries equation with loaded termsand a derivation of an analog of Dubrovin’s system of differential equations are proposed. Itis shown that the sum of a uniformly convergent function series constructed by solving theDubrovin system of equations and the first trace formula actually satisfies the loaded nonlinearKorteweg–de Vries equation. In addition, we prove that if the initial function is a real π-periodicanalytic function, then the solution of the Cauchy problem is a real analytic function in thevariable x as well, and also that if the number π/n, n ∈ N, n ≥ 2, is the period of the initialfunction, then the number π/n is the period for solving the Cauchy problem with respect to thevariable x.

Artificial Neural Network-Based Computational Algorithm of Inverse Sumudu Transform Applied to Surface Transient Electromagnetic Sounding Method

Abstract ––The paper discusses the results of the development of a deep learning-based algorithm of the inverse Sumudu transform applied to the problem of on-ground non-stationary electromagnetic sounding. The Sumudu transform has potential for solving forward geoelectric problems in three-dimensional earth models because, unlike using the Laplace or Fourier transform, the Sumudu image of a real function is also a real function. Thus, there is no need to use complex numbers in subsequent calculations, which reduces computational costs and memory requirements in case of successful determination of the Sumudu image of the function. The disadvantages of the approach include the absence of an explicit method for calculating the inverse transform. The inversion can be done by solving the corresponding Fredholm integral equation of the first kind, but this is a poorly conditioned task leading to high requirements for the accuracy of the Sumudu image. The use of modern machine learning techniques can provide a method that is more robust to noise in the input data. This paper describes the process of creating a training dataset and developing a neural network algorithm; we evaluate the accuracy and performance of the obtained solution. The proposed method can contribute to the development of new approaches to physical processes modeling as well as to analysis, processing and interpretation of measured geophysical data.

Identifying oil price shocks with global, developed, and emerging latent real economy activity factors

SummaryThis paper proposes an identification strategy for international oil price shocks while accounting for the heterogeneous sources of oil demand from global, developed, and emerging economies. Unlike existing works, we isolate global oil demand shocks, associated with a global real economic activity factor, from oil demand shocks originating specifically from developed and emerging economies, associated with real economic activity factors within these two groups of economies. The paper uses a structural factor‐augmented vector autoregression (FAVAR) model with latent global and specific factors to model crude oil demand and supply. To identify the shocks, we extract real economic activity factors from a large panel of emerging and developed economies' real activity variables using a two‐level factor model. The paper shows how structural shocks can be identified by solving equations that arise from economically meaningful zero restrictions on the impact matrix of the reduced‐form FAVAR model innovations. The empirical application shows that identifying the international oil demand shocks based on the global and specific latent factors is essential to appropriately quantify their heterogeneous impacts on these factors, the crude oil production, and the real oil price.

Theory of Functions of Several Real Variables and Its Applications

Известно, что результаты об универсальной дискретизации квадратичной нормы по значениям в точках полезны в разреженном восстановлении функций по значениям в точках с ошибкой, измеряемой в квадратичной норме. В работе продемонстрировано, как результаты об универсальной дискретизации равномерной нормы по значениям в точках и недавние результаты об универсальном представлении по значениям в точках позволяют предъявить хорошие универсальные методы восстановления по значениям в точках периодических функций нескольких переменных из анизотропных классов Соболева и Никольского. Наиболее точные результаты получены в случае функций двух переменных, где для восстановления используются множества точек Фибоначчи.

Ab-initio calculation of halogen elements effect on the behavior of new double perovskite Cs2InSbX6 (X = F, Cl, Br, I): 1st part structural and optoelectronic properties

In recent years, there has been a growing fascination with lead-free perovskite materials, particularly in the realms of solar energy and photonics. It is imperative to conduct comprehensive theoretical investigations of these materials to effectively guide experimental pursuits. In this research, we harnessed the power of density functional theory (DFT) calculations, employing the Wien2k code, to delve into the distinctive characteristics of double-perovskite halides Cs2InSbX6 (X = F, Cl, Br, I). The viability and stability of their cubic structures were meticulously assessed, taking into consideration essential metrics such as the tolerance factor, octahedral factor and formation energy. Notably, the pronounced influence of spin–orbit coupling necessitated gap energy adjustments, achieved through a dual-pronged approach utilizing the generalized Perdew–Burke–Ernzerhof gradient approximation (PBE-GGA) and the modified Becke-Johnson (mBJ) exchange potential. The intricacies of band structure and state density were scrutinized using the GGA + mBJ method. The comprehensive findings elucidate that these compounds manifest fundamental electronic bandgaps spanning a range from 0.26 to 2.67 eV. Furthermore, they exhibit remarkably low carrier effective masses and a substantial degree of band dispersion. Of significance is the profound influence of halogen atom substitutions on their optical properties. Notably, a high absorption coefficient in the ultraviolet spectrum and the presence of a negative real dielectric function provide strong evidence for the adoption of metallic properties within a specific energy range. These compelling outcomes underscore the potential of these materials as highly promising candidates for a diverse array of photonic applications.