Some Properties of the Basins of Attraction of the Newton’s Method for Simple Nonlinear Geodetic Systems

The research presented in this paper concerns the determination of the attraction basins of the Newton’s iterative method which was used to solve the non-linear systems of observational equations associated with the geodetic measurements. The authors considered simple observation systems corresponding to the intersections, or linear and angular resections, used in practice. The main goal was to investigate the properties of the sets of convergent in the initial points of the applied iterative method. An important issue regarding the possibility of automatic and quick selection of such points was also considered. Therefore, the answers to the questions regarding the geometric structure of the basins, their limitations, connectedness or self-similarity were sought. The research also concerned the iterative structures of the basins, i.e. maps of the number of iterations which are necessary to achieve the convergence of the Newton’s method. The determined basins were compared with the areas of convergence that result from theorems on the convergence of the Newton’s method, i.e. the conditions imposed on the eigenvalues and norms of the matrices of the studied iterative systems. One of the essential results of the research is the indication that the obtained basins of attraction contain areas resulting from the theoretical premises and their diameters can be comparable with the sizes of the analyzed geodetic structures. Consequently, in the analyzed cases it is possible to construct methods that enable quick selection of the initial starting points or automation of such selection. The paper also characterizes the global convergence mechanism of the Newton’s method for disconnected basins and, as a consequence, the non-local initial points, i.e. located far from the solution points.

Research on the Spatial Differences and Convergence Mechanism of Urban Land Use Efficiency under the Background of Regional Integration: A Case Study of the Yangtze River Economic Zone, China

Revealing the spatial differences and convergence mechanism of urban land use efficiency (ULUE) under the background of regional integration is of great significance for exploring the coordinated promotion path of ULUE. We attempted to build a theoretical framework to interpret ULUE spatial convergence under the background of regional integration and build a ULUE “green” evaluation system under multi-objective constraints. Based on this, we employed the super efficiency slack-based model (SBM), exploratory spatial data analysis, and spatial convergence model incorporated into the spatial weight matrix to re-examine the true level, spatial differences, and convergence mechanism of ULUE in the Yangtze River Economic Zone from 2003 to 2019 on a city scale. The results show that: (1) during the investigation period, ULUE in the Yangtze River Economic Zone has obvious spatial disequilibrium and spatial correlation characteristics; (2) there are absolute β-space convergence and conditional β-space convergence of ULUE in the whole Yangtze River Economic Zone and its upstream, midstream, and downstream areas; (3) driven by government management, industrial development, and spatial error effects, the convergence time of ULUE in the whole Yangtze River Economic Zone and its upstream, midstream, and downstream areas is obviously shortened.

Numerical methods for solving the equivalent inclusion equation in semi-analytical models

Equivalent inclusion method is the basis for semi-analytical models in tackling inhomogeneity problems. Equivalent eigenstrains are obtained by solving the consistency equation system of the equivalent inclusion method and then stress disturbances caused by inhomogeneities are determined. The equivalent inclusion method equation system can only be solved numerically, but the current fixed-point iteration method may not be able to achieve deep convergence when the Young's modulus of inhomogeneity is lower than that of the matrix material. The most significant innovation of this paper is to reveal the non-convergence mechanism of the current method. Considering the limitation, the Jacobian-free Newton Krylov algorithm is selected to solve the equivalent inclusion method equation. Results indicate that the new algorithm has significant advantages of computing accuracy and efficiency compared with the classic method.

Catch-up and Convergence: Mechanism Design for Economic Development

A globalization process can be conceived as an evolving distributed algorithmic mechanism design (DAMD) that induces technology racing with natural catch-up processes of regional or country-wide competition. We describe the architecture of DAMD as the basis for development economics that lead to natural ongoing shifts in industrial performance and catch-up development. The link between implementation of DAMD and a dynamic system of country-wide industrial evolution is essential for understanding the diverse pattern of inter-country or inter-regional competition. By selectively reviewing a cross section of the catch-up literature on economic growth it is shown which essential elements of long-run sustainable growth dominate to achieve superior performance and why informationally efficient mechanism design of the Hayek-Hurwicz type is a superior vehicle for industry based economic growth in a globalized economy.

Accommodative-Convergence Mechanism failure in HIV-Positive Non Presbyopic Patient on Highly Active Anti-Retroviral Therapy: A case report

Purpose: Accommodative-convergence mechanism failure could occur in non presbyopic HIV- sero positive patients on Highly Active Anti-Retroviral Therapy (HAART). This could be due to either direct neuronal infection by HIV, pathologic changes of the lens or the ciliary body or adverse effects of some individual drugs constituting the HAART regimen on the cranial nerves which play vital roles in the mechanism of accommodation and convergence. Case report: This is a case report of an accommodative- convergence mechanism failure in HIV positive non presbyopic 32-year-old male patient that was on HAART for more than five years. He presented with distance visual acuity (VA) of OD: 6/9 +2, OS: 6/9, and near visual acuity (NVA) of N24 both eyes, 3Δ esophoria at distance and 4Δ esophoria at near. Amplitude of accommodation (AA) was 3.50D and accommodative convergence/accommodation (AC/A) ratio was 6/1. Following comprehensive evaluation, his refractive correction was OD: Plano/-0.50DC X 180 6/5 and OS: Plano/-0.50DC X 90 6/5 at distance with near addition (Add) 2.50D N5. This was prescribed for regular wear in form of D-Top bifocal lens. Conclusion: These findings showed that HIV sero-positive adults on HAART could develop accommodativeconvergence mechanism failure, which may be characterized by low amplitude of accommodation, receded near point of convergence and high non presbyopic reading addition. These conditions may be under-recognized and need for reading addition of a non presbyopic age is often overlooked. Key Words: Accommodative-Convergence, HIV, Lateral Phoria, Refractive error.

Cognitive diagnosis of cultural and rural tourism convergence

Neural networks are widely used in the field of cognitive diagnosis. Cognitive diagnosis can diagnose the subjects’ knowledge of cognitive attributes according to their responses, so as to obtain the specific cognitive status of the subjects and provide remedial measures. The studies on the convergence of cultural industry and tourism industry are emerging, but the theoretical system needs to be improved. The research on the convergence mechanism between cultural industry and tourism industry can complement each other on the basis of independent theoretical system, which establishes relationship between the two theoretical systems. Based on the adaptive neural network algorithm and from the perspective of blockchain, this study takes cultural industry and rural tourism industry as examples to diagnose the industry convergence of rural cultural industry and rural tourism industry development, which will further consolidate the theoretical basis for the convergence and development of tourism industry and cultural industry, as well as contribute to promoting development of industry convergence.

Genome-Wide CRISPR Screen Reveals Autophagy Disruption as the Convergence Mechanism That Regulates the NRF2 Transcription Factor

ABSTRACT The nuclear factor (erythroid 2)-like 2 (NRF2 or NFE2L2) transcription factor regulates the expression of many genes that are critical in maintaining cellular homeostasis. Its deregulation has been implicated in many diseases, including cancer and metabolic and neurodegenerative diseases. While several mechanisms by which NRF2 can be activated have gradually been identified over time, a more complete regulatory network of NRF2 is still lacking. Here we show through a genome-wide clustered regularly interspaced short palindromic repeat (CRISPR) screen that a total of 273 genes, when knocked out, will lead to sustained NRF2 activation. Pathway analysis revealed a significant overrepresentation of genes (18 of the 273 genes) involved in autophagy. Molecular validation of a subset of the enriched genes identified 8 high-confidence genes that negatively regulate NRF2 activity irrespective of cell type: ATG12, ATG7, GOSR1, IFT172, NRXN2, RAB6A, VPS37A, and the well-known negative regulator of NRF2, KEAP1. Of these, ATG12, ATG7, KEAP1, and VPS37A are known to be involved in autophagic processes. Our results present a comprehensive list of NRF2 negative regulators and reveal an intimate link between autophagy and NRF2 regulation.