Residue Regulating Homotopy Method for Strongly Nonlinear Oscillator

It is highly desired yet challenging to obtain analytical approximate solutions to strongly nonlinear oscillators accurately and efficiently. Here we propose a new approach, which combines the homtopy concept with a “residue-regulating” technique to construct a continuous homotopy from an initial guess solution to a high-accuracy analytical approximation of the nonlinear problems, namely the residue regulating homotopy method (RRHM). In our method, the analytical expression of each order homotopy-series solution is associated with a set of base functions which are pre-selected or generated during the previous order of approximations, while the corresponding coefficients are solved from deformation equations specified by the nonlinear equation itself and auxiliary residue functions. The convergence region, rate and final accuracy of the homotopy are controlled by a residue-regulating vector and an expansion threshold. General procedures of implementing RRHM are demonstrated using the Duffing and Van der Pol-Duffing oscillators, where approximate solutions containing abundant frequency components are successfully obtained, yielding significantly better convergence rate and performance stability compared to the other conventional homotopy-based methods.

Climatological Features of Squall Line at the Borneo Coastline during Southwest Monsoon

Borneo Squall Line (BSL) is a disaster risk associated with intense rain and wind gust that affect the activities and residence near the northern coast of Borneo. Using 3-hourly rainfall from Tropical Rainfall Measuring Mission (TRMM) 3B42V7 during southwest monsoon season (May–September) from 1998–2018, a total of 629 squall days were identified. Their monthly and annual average was 6 and 30 days, respectively, with July representing the month with the highest number of squall line days. BSL is frequently initiated during midnight/predawn and terminated in the morning. Composite analyses of BSL days using the daily winds from the European Centre for Medium-Range Weather Forecasts (ECMWF) ERA-Interim revealed that lower tropospheric wind convergence is a crucial controlling factor for BSL formation. The position of the monsoon trough closer to the equatorial South China Sea (SCS), and strong westerly and south-westerly winds played an important role in creating this wind convergence region. Analyses of tropical cyclone (TC) data from the Regional Specialized Meteorological Centre (RSMC), Tokyo showed that nearly 72% of BSL occurred with the presence of TC. Spectral analysis exhibited prominent frequencies mainly in the 3–4- and 6-year time scale, which likely reflected the influence of interannual modulation of El-Niño Southern Oscillation (ENSO). Correlation coefficient between squall days and Sea Surface Temperature (SST) anomalies indicated that BSL increased after La-Niña events. This study is expected to have implications for real-time squall line forecasting in Malaysia and contributes toward a better understanding of BSL.

Insights Into the Environmental Impact on Genetic Structure and Larval Dispersal of Crown-of-Thorns Starfish in the South China Sea

The coral-eating crown-of-thorns starfish (COTS; Acanthaster spp.) play a major role in coral reef degradation in the Indo-Pacific region. However, the impacts of environmental factors on the phylogenetic and genetic characteristics of COTS in the northern Indo-Pacific convergence region remains unclear. We used mitochondrial DNA (mtDNA) and microsatellite markers to analyze the phylogenetic relationship, demographic history, genetic diversity and genetic structure of COTS in the South China Sea (SCS) and explored the impact of environmental factors on historical population expansion, genetic differentiation and larval dispersal. There was a clear signature of a population expansion in the SCS using the mtDNA marker. According to microsatellite loci analysis, COTS have high genetic diversity in the SCS. STRUCTURE analysis indicated that COTS in the Pacific Ocean can be divided into four subgroups: the SCS, Western Pacific, Pacific equatorial current affected zone, and Pacific insular atolls populations in the Pacific Ocean. Fst-statistical analysis revealed positive correlations between the Fst values and geographic isolation for all sampling sites. Additionally, there were no clear associations between the Fst values and chlorophyll a concentrations among coral reefs in the SCS; however, there were significant positive associations between the Fst values and particulate organic carbon (POC) concentrations within small geographic distances. These results suggest that COTS underwent historical population expansion after the Last Glacial Maximum, possibly followed by coral population expansion. The genetic structure of COTS populations may have been shaped by distinct nutrient concentrations, particularly those of POC, over small geographic distances. Moreover, ocean currents provide a potential dispersal mechanism for COTS larvae in the SCS. This study demonstrates that environmental and oceanographic factors play important roles in shaping the genetic characteristics and larval dispersal of COTS populations in the northern Indo-Pacific convergence region.

Fabric defect detection with an attention mechanism based on hard sample training

In view of the various types of fabric defects, and the problems of confusion, density unevenness and small target defects, which are difficult to detect, this paper builds a deep learning defect detection network incorporating an attention mechanism. The data augmentation strategy is used to enrich the number of samples of each defective type, and the enriched samples were extracted by the feature extraction network integrated with the attention mechanism, which can improve the feature extraction ability of confusable defect types and small defect types. Region proposal generation generates a proposal box for extracted features, and adds an online hard example mining strategy to re-learn hard examples to accelerate network convergence. Region feature aggregation maps the proposal box to the feature map to obtain the region of interest. Finally, the defect features are classified and the bounding boxes are regressed. The results show that this algorithm can effectively detect 39 categories of fabric defects with a detection speed of 0.085 s and a detection accuracy of 0.9338.

Comment in Reply to "On the complexity of extending the convergence region for Traub’s method"

This comment is in reply to the paper “On the complexity of extending the convergence region for Traub’s method” [1]. In complexity science, from the mathematical perspective, discussions of complexity often concern algorithmic complexity such as in the paper responded to here [2]. But this is only one of the kinds of complexity that exists even in the mathematical domain. There is also the complexity in the behavior of a system of equations; there is the complexity of the reasoning or algorithm required to understand a system of equations (“understand” interpreted here as defining the problem needing to be solved); and, as mentioned, there is the complexity of the reasoning or algorithm required to solve a system of equations.

Effects of Fences and Green Zones on the Air Flow and PM2.5 Concentration around a School in a Building-Congested District

We investigated the effects of wall- and tree-type fences on the airflow and fine particular matter (PM2.5) concentration around a school using a computational fluid dynamics (CFD) model. First, we validated the simulated wind speeds and PM2.5 concentrations against measured values, and the results satisfied the recommended criteria of the statistical validation indices used. Then, we evaluated the fence effects for 16 inflow directions by conducting numerical simulations with different fence types and heights. With east–southeasterly inflow, relatively high PM2.5 from the road was transported to the school. However, the wall-type fence prevented the PM2.5 from the road from entering the school, and the PM2.5 concentration decreased significantly downwind of the fence. With east–northeasterly inflow, the horizontal wind speed decreased due to the drag caused by the tree-type fence, resulting in a shift in the flow convergence region. The PM2.5 concentration decreased in the region of strengthened upward flow. This occurred because the number of pollutants transported from the background decreased. A comparison of the two fence types revealed that the effect of the tree-type fence on inbound pollutants was more significant, due to increased upward flows, than the effect of the wall-type fence.

Smart Specialisation Strategies and Regional Convergence: Spanish Extremadura after a Period of Divergence

Smart specialization strategies are a new EU approach to cohesion policy, meant to deliver growth and development at EU national and regional level. Bearing in mind its focus on place-based development strategies, this paper intends to shed some light on its appropriateness to tackle uneven development and regional growth divergence. The paper showcases Spanish Extremadura growth trajectory. Extremadura is a poor region in the European context that between 2008 and 2014 diverged from the EU average, despite being eligible for EU funding as a convergence region by cohesion policy. In the 2014–2020 programming period, there was a positive dynamic at the beginning, but from 2017 onwards convergence stopped, which indicates that thematic and regional programmes have not delivered results or have not compensated for higher growth level of other Spanish regions. Moreover, research and innovation strategies for smart specialization (RIS3) seem to have limited impacts on place-based economic transformation in less developed regions. From this example, the suitability of the smart specialisation strategy as the core of cohesion policy in the programming period is discussed. It concludes that this strategy is interesting for intermediate development regions with some industrial base but does not seem appropriate as a convergence driver for poorer regions.

A generalized multivariable Newton method

It is well known that the Newton method may not converge when the initial guess does not belong to a specific quadratic convergence region. We propose a family of new variants of the Newton method with the potential advantage of having a larger convergence region as well as more desirable properties near a solution. We prove quadratic convergence of the new family, and provide specific bounds for the asymptotic error constant. We illustrate the advantages of the new methods by means of test problems, including two and six variable polynomial systems, as well as a challenging signal processing example. We present a numerical experimental methodology which uses a large number of randomized initial guesses for a number of methods from the new family, in turn providing advice as to which of the methods employed is preferable to use in a particular search domain.

A theory of giant vortices

We elaborate a theory of giant vortices [1] based on an asymptotic expansion in inverse powers of their winding number n. The theory is applied to the analysis of vortex solutions in the abelian Higgs (Ginzburg-Landau) model. Specific properties of the giant vortices for charged and neutral scalar fields as well as different integrable limits of the scalar self-coupling are discussed. Asymptotic results and the finite-n corrections to the vortex solutions are derived in analytic form and the convergence region of the expansion is determined.