Radius Of Convergence Research Articles

The impact of innovative human capital on green growth convergence in China's regions from the perspective of space

The convergence of green growth is not only very important for the sustainable development of mankind, but also plays a key role in the coordinated development of eastern, Midwest regions of China. The effect of innovative human capital (IHC) on the convergence of regional green growth in China needs to be explored. This paper empirically explores the impact of IHC on the convergence of regional green growth in China from spatial perspective for the first time. Through the regression analysis of the convergence models, three main conclusions are obtained: (1) there are obvious conditional β space convergence characteristics of green growth among inter-provincial units in China. Under the spatial correlation expressed by distance weights and adjacent weights, the conditional β space convergence characteristics of green growth are quite different. (2) Compared with the adjacency weight, under the distance weight, the spatial diffusion effect of innovative knowledge and technologies created by IHC is stronger. (3) There is club convergence of green growth in the East and the Midwest regions, and the quantity and quality of IHC in the Midwest region play a stronger role in the convergence of green growth than in the East region. Based on the above conclusions, this paper proposes some policies for the East and Midwest regions.

Host-Virus Cophylogenetic Trajectories: Investigating Molecular Relationships between Coronaviruses and Bat Hosts.

Bats, with their virus tolerance, social behaviors, and mobility, are reservoirs for emerging viruses, including coronaviruses (CoVs) known for genetic flexibility. Studying the cophylogenetic link between bats and CoVs provides vital insights into transmission dynamics and host adaptation. Prior research has yielded valuable insights into phenomena such as host switching, cospeciation, and other dynamics concerning the interaction between CoVs and bats. Nonetheless, a distinct gap exists in the current literature concerning a comparative cophylogenetic analysis focused on elucidating the contributions of sequence fragments to the co-evolution between hosts and viruses. In this study, we analyzed the cophylogenetic patterns of 69 host-virus connections. Among the 69 host-virus links examined, 47 showed significant cophylogeny based on ParaFit and PACo analyses, affirming strong associations. Focusing on two proteins, ORF1ab and spike, we conducted a comparative analysis of host and CoV phylogenies. For ORF1ab, the specific window ranged in multiple sequence alignment (positions 520-680, 770-870, 2930-3070, and 4910-5080) exhibited the lowest Robinson-Foulds (RF) distance (i.e., 84.62%), emphasizing its higher contribution in the cophylogenetic association. Similarly, within the spike region, distinct window ranges (positions 0-140, 60-180, 100-410, 360-550, and 630-730) displayed the lowest RF distance at 88.46%. Our analysis identified six recombination regions within ORF1ab (positions 360-1390, 550-1610, 680-1680, 700-1710, 2060-3090, and 2130-3250), and four within the spike protein (positions 10-510, 50-560, 170-710, and 230-730). The convergence of minimal RF distance regions with combination regions robustly affirms the pivotal role of recombination in viral adaptation to host selection pressures. Furthermore, horizontal gene transfer reveals prominent instances of partial gene transfer events, occurring not only among variants within the same host species but also crossing host species boundaries. This suggests a more intricate pattern of genetic exchange. By employing a multifaceted approach, our comprehensive strategy offers a nuanced understanding of the intricate interactions that govern the co-evolutionary dynamics between bat hosts and CoVs. This deeper insight enhances our comprehension of viral evolution and adaptation mechanisms, shedding light on the broader dynamics that propel viral diversity.

Tracy-Widom Distribution in Four-Dimensional Supersymmetric Yang-Mills Theories.

Various observables in different four-dimensional superconformal Yang-Mills theories can be computed exactly as Fredholm determinants of truncated Bessel operators. We exploit this relation to determine their dependence on the 't Hooft coupling constant. Unlike the weak coupling expansion, which has a finite radius of convergence, the strong coupling expansion is factorially divergent, necessitating the inclusion of nonperturbative, exponentially small corrections. We develop a method to systematically compute these corrections and discuss the resurgent properties of the resulting transseries.

Local convergence of a two-step Gauss-Newton Werner-type method for solving least squares problems

The aim of this paper is to extend the applicability of a two-step Gauss-Newton-Werner-type method (TGNWTM) for solving nonlinear least squares problems. The radius of convergence, error bounds and the information on the location of the solution are improved under the same information as in earlier studies. Numerical examples further validate the theoretical results.

Estimates on the convergence of expansions at finite baryon chemical potentials

Convergence of three different expansion schemes at finite baryon chemical potentials, including the conventional Taylor expansion, the Padé approximants, and the T′ expansion proposed recently in lattice QCD simulations, have been investigated in a low energy effective theory within the functional renormalization group approach. It is found that the convergence of the T′ expansion and the Padé approximants is consistent with the conventional Taylor expansion, within the expansion orders considered in this work. Furthermore, we find that the consistent regions of the three different expansions are in agreement with the convergence radius of the Lee-Yang edge singularities. Published by the American Physical Society 2024

Multistep Iterative Methods for Solving Equations in Banach Space

The novelty of this article lies in the fact that we extend the use of a multistep method for developing a sequence whose limit solves a Banach space-valued equation. We suggest the error estimates, local convergence, and semi-local convergence, a radius of convergence, the uniqueness of the required solution that can be computed under ω-continuity, and conditions on the first derivative, which is on the method. But, earlier studies used high-order derivatives, even though those derivatives do not appear in the body structure of the proposed method. In addition to this, they did not propose computable estimates and semi-local convergence. We checked the applicability of our study to three real-life problems for semi-local convergence and two problems chosen for local convergence. Based on the obtained results, we conclude that our approach improves its applicability and makes it suitable for challenges in applied science.

On the analytic extension of three ratios of Horn's confluent hypergeometric function $\mathrm{H}_7$

In this paper, we consider the extension of the analytic functions of two variables by special families of functions — continued fractions. In particular, we establish new symmetric domains of the analytical continuation of three ratios of Horn's confluent hypergeometric function $\mathrm{H}_7$ with certain conditions on real and complex parameters using their continued fraction representations. We use Worpitzky's theorem, the multiple parabola theorem, and a technique that extends the convergence, already known for a small domain, to a larger domain to obtain domains of convergence of continued fractions, and the PC method to prove that they are also domains of analytical continuation.

Mergers and acquisitions, knowledge base and technological trajectories. An exploratory study in the wind energy sector

ABSTRACT The wind energy sector has increased its technological complexity for the last 20 years, with new technological and convergent domains like advanced materials, complex simulation, and artificial intelligence. In this context, mergers, and acquisitions (M&A) have become a key channel for companies in the sector to absorb new knowledge and develop complementary capabilities. The aim of this article is to trace the recent trajectory of the sector’s knowledge base and to analyze the role of M&A, specially of New Technology Based Firms in the generation of new capabilities through knowledge recombination. Using co-occurrence networks on a unique database of 1,299 companies in the wind sector and their acquired companies, we developed a methodological approach to investigate the trajectory of the wind sector at a global level. The empirical analysis verifies that acquisitions belonging to ‘unrelated’ sectors contribute significantly to the diversification and complexification of the sector’s knowledge base over time.

Optimal Transport Map With Prescribed Direction Indicator for Seismic Full‐Waveform Inversion

AbstractThe quadratic Wasserstein (W2) metric has been proposed as a promising misfit function to mitigate cycle‐skipping phenomena in full‐waveform inversion. Mathematically, we demonstrate that the smoothness of the W2‐based adjoint source is two orders of magnitude higher than that based on L2‐norm, which guarantees a larger convergence radius of related inverse problems. However, the oscillatory characteristics of seismic signals and subsequent operations of transforming them into probability densities would decrease the accuracy of the optimal transport map T(t) and exacerbate the nonconvexity of the misfit function. To tackle these challenges, we propose the concept of prescribed direction indicator, which indicates the properly matching direction from predictions to observations, in order to correct inaccurate T(t). 1D synthetic examples suggest that reasonable bijection can be constructed through the proposed method. Numerical experiments demonstrate that it works well during optimization procedures, including enlarging the convergence radius of the inverse problem, improving the computational efficiency and enhancing the reliability of inversion results.

Sensorless Capability Expansion for SPMSM Based on Inductance Parameter Identification

Pulsating high-frequency voltage injection can be used for the sensorless control of a surface-mounted permanent magnet synchronous motor (SPMSM) at zero- and low-speed ranges. However, the sensorless capability still faces challenges to the requirements of industrial application, especially at heavy load status. Aiming at this issue, this article proposes a sensorless capability expansion method for an SPMSM based on inductance parameter identification. Firstly, incremental inductances at the d-q-axis and cross-coupling inductance are identified offline by three steps combining the rotating high-frequency voltage injection and pulsating high-frequency voltage injection. Using a polynomial curve fitting algorithm, apparent inductances are calculated. Secondly, positive DC current injection at the d-axis is proposed to enhance the saliency ratio based on the analysis of parameter identification results. Compared with the conventional id = 0 or id < 0 method, the saliency ratio is enhanced obviously when a positive DC current is injected at the d-axis. Then, the convergence region of the sensorless control method at heavy load status is expanded and the accuracy of rotor position estimation is improved using the proposed method. Finally, the experimental results validate that the sensorless capability of the SPMSM is expanded.

THE ROLE OF BANKING SYSTEM IN PROVINCIAL ECONOMIC DEVELOPMENT: A STUDY OF TURKIYE, FROM THE 70S TO THE 2000S

This research examines the relationship between banking activities and provincial economic development. In particular, the study offers insight on the nature of the regional economic development discrepancies in Turkiye. The study finds that, despite the trend towards decentralisation that takes place in regional economic policies, the banking system adopts centralisation policies. Using dynamic generalised method of moment (GMM) estimates, we evaluated a unique data set including 39 years of provincial demographic, socioeconomic, and financial factors in Turkey. The study demonstrates that the banking intermediation is detrimental to provincial development. The Turkish banking system’s hierarchical structure prevents financial intermediaries from fulfilling their role in fostering development. Consolidation and concentration strategies must be reassessed, since they tend to favour centralisation, which has been shown to be inefficient for regional convergence. The results also suggest that branch managers should be granted greater decision-making authority to make better use of locally produced information when approving or rejecting projects, which would eventually lead to a reduction in provincial disparities.

Generating functions of non-backtracking walks on weighted digraphs: Radius of convergence and Ihara's theorem

It is known that the generating function associated with the enumeration of non-backtracking walks on finite graphs is a rational matrix-valued function of the parameter; such function is also closely related to graph-theoretical results such as Ihara's theorem and the zeta function on graphs. In Grindrod et al. [13], the radius of convergence of the generating function was studied for simple (i.e., undirected, unweighted and with no loops) graphs, and shown to depend on the number of cycles in the graph. In this paper, we use technologies from the theory of polynomial and rational matrices to greatly extend these results by studying the radius of convergence of the corresponding generating function for general, possibly directed and/or weighted, graphs. We give an analogous characterization of the radius of convergence for directed (unweighted or weighted) graphs, showing that it depends on the number of cycles in the undirectization of the graph. We also consider backtrack-downweighted walks on unweighted digraphs, and we prove a version of Ihara's theorem in that case. Finally, for weighted directed graphs, we provide for the first time an exact formula for the radius of convergence, improving a previous result that exhibited a lower bound, and we also prove a version of Ihara's theorem.

Self-similar mass accretion history in scale-free simulations

ABSTRACT Using a scale-free N-body simulation generated with the abacusN-body code, we test the robustness of halo mass accretion histories via their convergence to self-similarity. We compare two halo finders, rockstar and compaso. We find superior self-similarity in halo mass accretion histories determined using rockstar, with convergence to 5 per cent or better between $\sim\!\! 10^2$ and $10^5$ particles. For compaso, we find weaker convergence over a similar region, with at least 10 per cent between $\sim\!\! 10^2$ and $10^4$ particles. Furthermore, we find that the convergence to self-similarity improves as the simulation evolves, with the largest and deepest regions of convergence appearing after the scale factor quadrupled from the time at which non-linear structures begin to form. With sufficient time evolution, halo mass accretion histories are converged to self-similarity within 5 per cent with as few as $\sim\!\! 70$ particles for compaso and within 2 per cent for as few as $\sim\!\! 30$ particles for rockstar.

Mixing and Thermal Transport Behavior in a Pin or Non-Pin Extruder Equipped with a Field Synergy Elongation Screw.

The ductile forming process of a polymer in a standard screw extruder and pin-barrel extruder, equipped with or without a field synergy elongation screw, was investigated by the finite element method. In order to assess the mixing and heat transfer capabilities of screws, characteristic parameters such as the mixing efficiency, segregation scale, and temperature distribution of different structures were analyzed and compared. The results indicated that the flow pattern of the polymer melt in the extruder was significantly influenced by the screw structure and was improved by the newly designed field synergy screw configuration, which brought a desirable elongational flow to enhance the radial convection. This was attributed to the unique radial wedge-shaped repeated convergence region of the field synergy elongation screw, increasing the synergistic effect between the velocity field, velocity gradient field, and temperature gradient field and thus improving the heat transfer and mixing efficiency. After adding barrel pins, the flow was forced to split, resulting in a more significant stretching effect on the melt. The field synergy effect in the pin mixed region was strengthened, which further increased the heat and mass transfer efficiency of the screw. However, increasing barrel pins could also lead to undesired temperature fluctuation and flow resistance, which have a negative impact on the melt uniformity. This study offers an important reference for optimizing screw structure to obtain strong mixing and heat transfer performances.

Regional disparities in the European Union. A machine learning approach

We investigate the hypothesis of regional convergence in the per-capita GDP in 242 European regions (NUTS2) during the 2000–2021 period. The literature shows mixed results, from absolute convergence towards a joint long-run distribution to multiple regimes (convergence club). Our results show a broad convergence to an unimodal distribution. Although the GDP distribution was characterized by a twin-peak property in 2000, it tends to disappear over time, bringing, in 2021, to an unimodal distribution. Physical and human capital is the most responsible for the convergence process and the EU cohesion funds. To empirically investigate the question, we first apply alternative techniques of cluster identification. Later, we assess whether clusters and covariates affect the per-capita GDP. We use a novel machine learning algorithm (GPBoost) instead of the more traditional techniques used in the current literature. The results show that a convergence process is at work; physical and human capital are mainly responsible for the gdp explanation. but eu funds play a relevant role as well. moreover, complementarities do exist among these variables.

Schwarzschild Black Hole from Perturbation Theory to All Orders.

Applying the quantum field theoretic perturbiner approach to Einstein gravity, we compute the metric of a Schwarzschild black hole order by order in perturbation theory. Using recursion, this calculation can be carried out in de Donder gauge to all orders in Newton's constant. The result is a geometric series which is convergent outside a disk of finite radius, and it agrees within its region of convergence with the known de Donder gauge metric of a Schwarzschild black hole. It thus provides a first all-order perturbative computation in Einstein gravity with a matter source, and this series converges to the known nonperturbative expression in the expected range of convergence.

Patterns of neuronal activation following ethanol-induced social facilitation and social inhibition in adolescent cFos-LacZ male and female rats

Alcohol-associated social facilitation together with attenuated sensitivity to adverse alcohol effects play a substantial role in adolescent alcohol use and misuse, with adolescent females being more susceptible to adverse consequences of binge drinking than adolescent males. Adolescent rodents also demonstrate individual and sex differences in sensitivity to ethanol-induced social facilitation and social inhibition, therefore the current study was designed to identify neuronal activation patterns associated with ethanol-induced social facilitation and ethanol-induced social inhibition in male and female adolescent cFos-LacZ rats. Experimental subjects were given social interaction tests on postnatal day (P) 34, 36, and 38 after an acute challenge with 0, 0.5 and 0.75 g/kg ethanol, respectively, and β-galactosidase (β-gal) expression was assessed in brain tissue of subjects socially facilitated and socially inhibited by 0.75 g/kg ethanol. In females, positive correlations were evident between overall social activity and neuronal activation of seven out of 13 ROIs, including the prefrontal cortex and nucleus accumbens, with negative correlations evident in males. Assessments of neuronal activation patterns revealed drastic sex differences between ethanol responding phenotypes. In socially inhibited males, strong correlations were evident among almost all ROIs (90 %), with markedly fewer correlations among ROIs (38 %) seen in socially facilitated males. In contrast, interconnectivity in females inhibited by ethanol was only 10 % compared to nearly 60 % in facilitated subjects. However, hub analyses revealed convergence of brain regions in males and females, with the nucleus accumbens being a hub region in socially inhibited subjects. Taken together, these findings demonstrate individual and sex-related differences in responsiveness to acute ethanol in adolescent rats, with sex differences more evident in socially inhibited by ethanol adolescents than their socially facilitated counterparts.

An efficient yet accurate optimization algorithm for thermal systems integrating heat current method and generalized Benders decomposition

Thermal system optimization is critical for energy conservation but challenging due to highly complicated systems and nonlinear governing equations. Herein, an efficient yet accurate optimization algorithm based on generalized Benders decomposition (GBD) is developed to address this challenge. It decomposes the entire optimization into a subproblem and a master problem. The subproblem performs the system simulation by developing a hybrid simulation method, which uses GBD and fixed-point iteration sequentially for acceleration. The master problem is constructed based on the gradients of the objective with respect to decision variables, where the solution of every iteration gives an approximation of the optimal solution. The two generated problems are iteratively solved in an alternating manner to converge towards the optimal solution. Test results of a supercritical carbon dioxide recompression system indicate that the hybrid simulation method expands the convergence region to ∼167 % which is nearly 4 times larger than that of the fixed-point iteration, and consumes about 10 % calculation time compared with sequential modular method. The optimization algorithm reproduces the results obtained from the genetic algorithm but reduces the calculation time for an order-of-magnitude and has higher stability. The high efficiency and accuracy suggest the proposed algorithm as a powerful system optimization tool.

Convergence region size research of television signal superposition iteration method for measurement machine vision system

Background. Image processing is used in machine vision measurement systems, which are widely used in industrial applications. One of the important tasks in processing is image superposition. Registration methods must fulfill two basic requirements: satisfactory registration quality and practical processing time. One of the methods that meets these requirements is iterative superposition. Aim. The aim is to study the size of the area (region of convergence) for the values of the parameters of the initial approximation, which ensures satisfactory superposition. The size of the region determines the performance of the iterative algorithm. Methods. The size of the region of convergence was determined experimentally: correlation analysis and statistical simulation. Results. Experiments have shown if a sampling step is no more than 1/10 of the size of the image fragment, then the probability of correct registration is almost equal to one. If this threshold is exceeded, then the probability decreases. Conclusion. The size of the region of convergence of the iterative image registration method has been established. It is possible to design processing algorithms and predict processing time by obtaining results. The superposition method was introduced into a machine vision system to recognize contact wire clamps on the railway. Image superposition in this system is carried out in real time.

Resilient Factor Graph-Based GNSS/IMU/Vision/Odo Integrated Navigation Scheme Enhanced by Noise Approximate Gaussian Estimation in Challenging Environments

The signal blockage and multipath effects of the Global Navigation Satellite System (GNSS) caused by urban canyon scenarios have brought great technical challenges to the positioning and navigation of autonomous vehicles. In this paper, an improved factor graph optimization algorithm enhanced by a resilient noise model is proposed. The measurement noise is resilient and adjusted based on an approximate Gaussian distribution-based estimation. In estimating and adjusting the noise parameters of the measurement model, the error covariance matrix of the multi-sensor fusion positioning system is dynamically optimized to improve the system accuracy. Firstly, according to the approximate Gaussian statistical property of the GNSS/odometer velocity residual sequence, the measured data are divided into an approximate Gaussian fitting region and an approximate Gaussian convergence region. Secondly, the interval is divided according to the measured data, and the corresponding variational Bayesian network and Gaussian mixture model are used to estimate the innovation online. Further, the noise covariance matrix of the adaptive factor graph-based model is dynamically optimized using the estimated noise parameters. Finally, based on low-cost inertial navigation equipment, GNSS, odometer, and vision, the algorithm is implemented and verified using a simulation platform and real-vehicle road test. The experimental results show that in a complex urban road environment, compared with the traditional factor graph fusion localization algorithm, the maximum improvement in accuracy of the proposed algorithm can reach 65.63%, 39.52%, and 42.95% for heading, position, and velocity, respectively.