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Against the backdrop of rapid population aging and significant demographic changes, cities are facing great challenges in providing healthcare resources for the elderly. Understanding the equity and spatial differentiation mechanisms between the demand and supply of healthcare resources for the elderly in cities, especially in rapidly urbanized areas, can help policymakers to promote the planning and construction of a ‘Just City’ and ‘Age-Friendly City’, safeguarding the human well-being of the elderly. This study combines outpatient appointment data classified by service type with community-scale demographic data to assess the equity in the supply of medical resources for the elderly in the city using a refined two-step moving search method. Taking Xiamen City as an example, we analyzed the spatial heterogeneity in the equity in the supply of different types of health care services for potential elderly patients in each community in the city. Then, we selected six driving factors to explore the underlying driving factors. The results showed that there were 308 communities (61.11%) with a high medical service balance of the internal medicine type for the elderly in Xiamen City, concentrated in the southwest of the whole area. There are only 157 communities with high medical service balance for the surgical type of medical services, concentrated in the central part and southwest of Xiamen City. For these two types of medical services, the number of communities with low medical service balance is 30 (5.95%) and 182 (36.11%), respectively. These communities are far away from the central city. Economic vitality is the most important driving factor in the spatial distribution pattern of equity in the balance of medical services for the elderly. Our study can provide quantitative information on the current situation evaluation and decision support for the development and design of a ‘Just City’ and ‘Age-Friendly City’ Planning.

Shape-constrained convex regression problem deals with fitting a convex function to the observed data, where additional constraints are imposed, such as component-wise monotonicity and uniform Lipschitz continuity. This paper provides a unified framework for computing the least squares estimator of a multivariate shape-constrained convex regression function in $\mathbb{R}^d$. We prove that the least squares estimator is computable via solving an essentially constrained convex quadratic programming (QP) problem with $(d+1)n$ variables, $n(n-1)$ linear inequality constraints and $n$ possibly non-polyhedral inequality constraints, where $n$ is the number of data points. To efficiently solve the generally very large-scale convex QP, we design a proximal augmented Lagrangian method (proxALM) whose subproblems are solved by the semismooth Newton method (SSN). To further accelerate the computation when $n$ is huge, we design a practical implementation of the constraint generation method such that each reduced problem is efficiently solved by our proposed proxALM. Comprehensive numerical experiments, including those in the pricing of basket options and estimation of production functions in economics, demonstrate that our proposed proxALM outperforms the state-of-the-art algorithms, and the proposed acceleration technique further shortens the computation time by a large margin., arXiv admin note: substantial text overlap with arXiv:2002.11410

Flexible sensors are core components of intelligent wearable technology, and they are rapidly developing. Among these, flexible force sensors use flexible sensing materials to convert stress and strain into electrical signals. However, when the ionic flexible force sensor is subjected to external mechanical force, it will cause uneven distribution in the internal ions and generate electrical signals. This can be used to resolve issues with sensors to distinguish the stress or strain direction, by applying positive and negative electric potential without an external power supply. In addition, this integration process is simple and convenient. This review article describes the working mechanism of ionic flexible force sensors and describes the materials and properties used in these sensors, including electrolyte layer materials and electrode materials. We then list the latest applications in the fields of health care, motion detection, intelligent 3D robots and so on. Finally, we highlight the current limitations and future development of ionic flexible force sensors, to simultaneously develop new materials and technology with improved sensitivity for mass production.

Introduction Low-concentration oxygen is an established way for the treatment of chronic obstructive pulmonary disease (COPD) with Type II respiratory failure. Hypercapnia can complicate both COPD exacerbations and stable COPD. Treating with noninvasive ventilation (NIV) can reduce carbon dioxide tension in arterial (PaCO2 ) in hypercapnic COPD. As an open system, high-flow nasal cannula oxygen (HFNC) is easy to tolerate and use. More researches are needed to focus on how HFNC is used to treat COPD patients with hypercapnic respiratory failure. Methods The Cochrane Library, Medline, EMBASE, and CINAHL database were retrieved from inception to October 2019. Eligible trials were clinical randomized controlled trials comparing the effects of HFNC and conventional oxygen on hypercapnic COPD patients. Two researchers assessed the quality of each study and extracted the data into RevMan 5.3 independently. The primary outcome was PaCO2 and the secondary outcome was PaO2 . Results Four RCTs with 329 patients were included. The research results indicated that PaCO2 in the HFNC group was similar to the conventional oxygen group. No significant difference were observed in PaCO2 (MD -0.98, CI: -2.67 to 0.71, Z = 1.14, p = 0.25) and PaO2 (MD -0.72, CI: -6.99 to 5.55, Z = 0.23, p = 0.82) between the HFNC group and conventional oxygen group. Conclusions Our meta-analysis showed no difference in PO2 and PCO2 between the HFNC and conventional oxygen. But we should treat this conclusion with caution because the number of studies and participants is small and, there is heterogeneity in the PaO2 and PCO2 measurements between stable and AECOPD.

Green infrastructure network (GIN) optimization is an effective measure to reduce the landscape fragmentation caused by rapid urbanization. However, there are few targeted and practical studies of GINs in high-density urban areas with a prominent contradiction between ecological construction and land scarcity, leading to insufficient feasibility of most optimization paths as they avoid practical contradictions (scarcity of land, high cost, etc.). As an effective way to economically increase green infrastructure, green roofs have been demonstrated to provide habitats and stepping stones to increase landscape connectivity for high-mobility organisms. However, few studies have applied green roofs to GIN optimization. To address this question, a new approach to optimize GINs was proposed from the perspective of integrating potential green roofs (PGRs). A complete and feasible workflow was also established to rapidly, accurately, and cost-effectively extract PGRs, scientifically evaluate the comprehensive landscape connectivity accounting for PGR isolation factors, and practically optimize GINs according to the spatial differentiation of PGRs with high landscape connectivity. This was done by integrating high-spatial-resolution remote sensing, machine learning, morphological spatial pattern analysis, landscape index method, and a minimum cumulative resistance model. A case study in a typical high-density urban area within the Beijing Fifth Ring Road, China demonstrated the applicability and implications of the workflow. The results clearly showed that the study area had a high potential for green roof retrofitting, PGRs with high landscape connectivity could effectively improve the GINs, and the spatial differentiation characteristics of the PGR network optimization benefits provided the scientific guidance for developing targeted ecological strategies. The new approach effectively improves the scientificity and implementability of GINs. It also provides a strong reference for landscape planning and ecological construction in other high-density urban areas facing the contradiction between ecological construction and land scarcity.

Food consumption is fundamental for urban households if they are to sustain production and daily life. Nitrogen resulting from food consumption has significantly contributed to pollutant emissions in urban ecosystems. Taking Xiamen city, a rapid urbanizing area of southeast China as a case study, we evaluated the food-sourced nitrogen consumption of households based on a large simple onsite questionnaire survey, as well as differences between households in the consumption of plant-based and animal-based foods. A material flow analysis (MFA) was conducted to simulate the urban metabolism of food-sourced nitrogen and environmental emissions among different income groups. The impacts of household attributes, plant-based food consumption, and animal-based food consumption on environmental nitrogen emissions were examined with a structural equation model (SEM). Our results show that the surveyed households’ diets were more plant-based and less animal-based. Aquatic products and livestock were the source of 43.7% of food-sourced nitrogen, and 84.5% of the food-sourced nitrogen was discharge into the environment through direct discharge and waste treatment. Soil, water, and air emissions accounted for 62.8%, 30.1%, and 7.1% of the food-sourced nitrogen, respectively. Household income, household size, and household area are all associated with accelerating increases of nitrogen emissions released into the environment, though middle-income group households have the highest food-sourced environmental nitrogen emissions. On this basis, we discuss how to better manage the urban metabolism of food-sourced nitrogen, so as to improve urban household consumption, lower nitrogen emissions, and improve food security.

The rational design of a novel and environmentally friendly photocatalytic composite for persistent pollutant removal, energy production and catalytic applications have attracted widespread interest. In this study, the new composite composed of KOH-modified biochar and g-C

Urbanization has significant effects to ecosystems in watersheds, but the link between surface water quality and the dissolved organic matter (DOM) composition is poorly understood. We investigated the fluorescent intensities (Fmax) of DOM components and examined their correlation with the water quality parameters in peri-urban (Zhangxi River) and urban (Lu River) watersheds in Ningbo, East China. DOM quality was measured by fluorescent excitation-emission matrices (EEMs) coupled with parallel factor analysis (PARAFAC). Terrestrial humic-like components (C1 and C2) and protein-like component (C3) were derived by the PARAFAC model. We found more serious water pollution (significantly higher values for most water quality parameters, i.e. chemical oxygen demand (COD), chlorophyll a (Chl-a), dissolved organic carbon (DOC), ammonia and total suspended solids (TSS)) in urban than peri-urban watersheds. However, there were no significant differences in the levels of total nitrogen (TN) and total phosphorus (TP) between the urban and peri-urban watersheds. The results showed that the urban watershed had higher terrestrial humic-like C1 (39%) and lower protein-like C3 (30%) than the peri-urban watershed, while the peri-urban watershed showed an inverse trend (33% and 37%, respectively). The results also revealed that the DOM fluorescent indices were significantly different between the peri-urban and the urban watersheds. Redundancy analysis (RDA) was applied to evaluate the correlation between DOM fluorescent indices and water quality parameters (i.e., COD, TN, TP, DOC). It revealed that the pollution sources and water quality correlated to the fluorescent indices and the C1-C3 DOM fluorescent components. A significant linear relationship between COD and C2 was found in both watersheds, suggesting that C2 might be a good COD indicator. Our results suggest that the distinctive DOM composition between the watersheds could be attributed to different human activities at both sites. The correlation between DOM fluorescent components and water quality can be assessed by the EEM-PARAFAC method, indicating considerable potential for the use of this technique to monitor surface water quality.

Urban spatial expansion poses a threat to regional ecosystems and biodiversity directly through altering the size, shape, and interconnectivity of natural landscapes. Monitoring urban spatial expansion using traditional area-based metrics from remote sensing provides a feasible way to quantify this regional ecological stress. However, variation in landscape-adjacency relationships (i.e., the adjacency between individual landscape classes) caused by urban expansion is often overlooked. In this study, a novel edge-based index (landscape-adjacency index, LAdI) was proposed based on the spatial-adjacency relationship between landscape patches to measure the regional ecological stress of urban expansion on natural landscapes. Taking the entire Yangtze River Delta Urban Agglomerations (YRD) as a study area, we applied the LAdI for individual landscape classes (Vi) and landscape level (LV) to quantitatively assess change over time in the ecological stress of YRD from 1990 to 2015 at two spatial scales: municipal scale and 5 km-grid scale. The results showed that the vulnerable zones (LV ≥ 0.6) were mainly distributed in the north of the YRD, and cultivated land was the most vulnerable natural landscape (Vi ≥ 0.6) at the 5 km-grid scale. The most vulnerable landscape at the municipal scale was cultivated land in 19 of 26 cities in each period, and that in the remaining 7 cities varied at distinct urbanization stages. We used scatter diagrams and Pearson correlation analysis to compare the edge-based LAdI with an area-based index (percent of built-up area, PB) and found that: LV and PB had a significant positive correlation at both the municipal scale and 5 km-grid scale. But there were multiple LVs with different values corresponding to one PB with the same value at the 5 km-grid scale. Both indexes could represent the degree of urban expansion; however, the edge-based metric better quantified ecological stress under different urban-sprawl patterns sharing the same percent of built-up area. As changes in land use affect both the size and edge effect among landscape patches, the area-based PB and the edge-based LAdI should be applied together when assessing the ecological stress caused by urbanization.

The development trend, market application, standards and regulations of vehicle operating system (VOS) technology at home and abroad are studied in this paper. Combined with the definition and classification of VOS, main characteristics of the most representative VOS at home and abroad are analyzed. Based on the domestic situation of VOS, the main problems existing in vehicle industry are analyzed, and suggestions of development strategy of domestic VOS are put forward.

Spectrograms are fundamental tools in time-frequency analysis, being the squared magnitude of the so-called short time Fourier transform (STFT). Signal analysis via spectrograms has traditionally explored their peaks, i.e. their maxima. This is complemented by a recent interest in their zeros or minima, following seminal work by Flandrin and others, which exploits connections with Gaussian analytic functions (GAFs). However, the zero sets (or extrema) of GAFs have a complicated stochastic structure, complicating any direct theoretical analysis. Standard techniques largely rely on statistical observables from the analysis of spatial data, whose distributional properties for spectrograms are mostly understood only at an empirical level. In this work, we investigate spectrogram analysis via an examination of the stochastic geometric properties of their level sets. We obtain rigorous theorems demonstrating the efficacy of a spectrogram level sets based approach to the detection and estimation of signals, framed in a concrete inferential set-up. Exploiting these ideas as theoretical underpinnings, we propose a level sets based algorithm for signal analysis that is intrinsic to given spectrogram data, and substantiate its effectiveness via extensive empirical studies. Our results also have theoretical implications for spectrogram zero based approaches to signal analysis. To our knowledge, these results are arguably among the first to provide a rigorous statistical understanding of signal detection and reconstruction in this set up, complemented with provable guarantees on detection thresholds and rates of convergence.

Urban agglomeration (the spread of cities into large agglomerations) has become the main form of urbanization in China, and natural ecosystems surrounding the urban areas are becoming degraded and fragmented as a result. Although ecological indicators have been widely used to assess the regional ecological stress resulting from urbanization, few of them consider spatial adjacency relationships between urban and natural landscapes. From this perspective a novel ecological indicator, the Eco-Erosion Index (EEI), was developed and applied to assess the regional ecological stress caused by urban agglomeration development across 26 cities in the Yangtze River Delta, China (YRD). We analyzed: i) temporal change in land use and land cover (LULC) and ecosystem services value (ESV) in YRD from 1990 to 2010, ii) spatiotemporal dynamics of EEI of YRD at different scales: provincial, municipal, and 5 km-grid, iii) inter-relationships between EEI and LULC and ESV to explore its effectiveness as an indicator. The results showed that urban agglomeration in YRD has led to increasing regional ecological stress from 1990 to 2010. EEI values increased from 0.197 in 1990 to 0.321 in 2010. The closer to Shanghai City, the greater the EEI values of the cities become. EEI is highly related with LULC and ESV but integrates these two variables as it represents both the spatial occupation and landscape adjacency effects. The EEI values demonstrate some scale effects, and EEI at fine scale provides useful information to guide sustainable urban landscape management.

The development of novel and green photocatalysts have attracted considerable attentions due to their excellent performance for environmental remediation, especially for the degradation of persistent pollutants. In this work, the biochar-supported K-doped g-C3N4 composites with the high photocatalytic activity under visible light irradiation was prepared by the calcination-impregnation method. The crystal structure, apparent morphology and functional group composition of the as-prepared photocatalytic materials were studied by X-ray diffraction (XRD), scanning electron microscopy (SEM) and Fourier transform infrared spectroscope (FTIR). Moreover, the characterization of UV-Vis diffuse reflectance spectra (UV-Vis DRS) and photoluminescence technique (PL) verified the good optical properties of resultant samples. Naphthalene was selected as the representative compound to evaluate the photocatalytic performance of the prepared photocatalysts under visible light irradiation. The evaluation results showed that the biochar-supported K-doped g-C3N4 composites exhibited excellent photocatalytic activity (82.19%). Moreover, the photocatalytic degradation rate basically remained unchanged after five cycles, indicating the good stability of the prepared photocatalysts. In addition, a possible mechanism for the photodegradation process was proposed on the basis of the main intermediates detected by gas chromatography-mass spectrometer (GC-MS). This study may provide a promising approach for the polycyclic aromatic hydrocarbon degradation by waste utilization of agricultural biomass and increasing the photocatalytic performance of pure g-C3N4.

The rational design of a novel and environmentally friendly photocatalytic composite for persistent pollutant removal, energy production and catalytic applications have attracted widespread interest. In this study, the new composite composed of KOH-modified biochar and g-C3N4 with different morphologies was successfully prepared with facile supramolecular self-assembly and thermal poly-condensation method. The characterization results of the as-prepared composites suggested that KOH-modified biochar had been well combined with g-C3N4 with different morphologies. These synthesized catalysts were used to degrade phenanthrene under visible light radiation. A-BC/g-C3N4-D performed best and removed 76.72% phenanthrene. Its first-order reaction rate constant was 0.355 h-1, which was 3.7 times higher than that of g-C3N4. A-BC/g-C3N4-D still exhibited a high photocatalytic activity after four cycles. Radical quenching results showed that superoxide radical (·O2-), hydroxyl radical (·OH) and hole (h+) could be used as active species in the redox reaction with phenanthrene. Based on the exploration results of gas chromatography-mass spectrometer (GC-MS), a possible reaction pathway of phenanthrene degradation was also proposed. This study provides a novel strategy for fabricating various high-performance photocatalysts and the removal of persistent organic pollutants.

Background Achieving urban sustainability is the ultimate destination of urban development. City rankings as one of the sustainability assessment tools have received increasing attention from the scientific community. However, few study assesses Chinese cities’ sustainability performance using the big data of existing city rankings. Aim This study aims to assess Chinese cities’ sustainability performances based on the outcomes of the existing internet big data of city rankings. Methods The outcomes of city rankings were used as the raw dataset. The “sustainability” of city rankings, city’s appearance frequency, and its ranking place were comprehensively considered during evaluation processes. By considering the above factors, the scores of different cities were calculated in terms of overall sustainability and domain sustainability. Furthermore, the GeoDetector was applied to explore the association between social-economic and overall ranking scores as well as the interrelation among TBL dimensions. Results Chinese cities’ sustainability performance was extremely uneven in spatial distribution. In terms of overall and domain sustainability, well-performing cities were aggregated in the Beijing-Tianjin-Hebei, the Yangtze River Delta, and the Pearl River Delta metropolitan regions. The top ten sustainable cities were Hangzhou, Beijing, Shenzhen, Guangzhou, Zhuhai, Hong Kong, Tianjin, Suzhou, and Xiamen. Most cities did not reach good coordination among the TBL dimensions, instead of developing well in one or two aspects. The results also revealed that current city rankings eyeing more economic and social development, while considering less environmental dimension. Moreover, TBL dimensions mutually reinforce each other in sustainable city construction. The environmental pillar played a critical role and interacting with other dimensions significantly enhanced urban sustainability. Conclusion The outcomes of existing city rankings can be used as a new resource to evaluate cities’ sustainability performance. Current city rankings in China are not systematically considered in terms of TBL dimensions. Cities should enhance the coordination among TBL pillars, and increase the attention on environmental dimension. More empirical studies involving big data of city rankings will contribute to a new perspective to promote the practice of sustainable urbanization in China.

There is in general good awareness of the potential role of green roofs to regulate urban thermal environments, but a lack of effective spatial modeling of this cooling effect for a given roof greening scheme at the city scale. This study proposes a simplified and feasible approach to simulate the cooling effect provided by green roofs as a mitigation option to combat urban heat island effects in high-density urban areas. In this study, we established a spatial model of the cooling effect of green roofs, which integrated remote sensing methods and a statistical model based on the law of diminishing marginal utility of the cooling efficiency of green roofs (DMUCE) deduced from previous studies. A case study in Xiamen City, China demonstrates the applicability and implications of the model. Our modeling clearly simulated the size and strength of the urban cool island and its variation under different green roof scenarios. We found that green roofs play an important part in moderating the thermal environment in areas where larger green spaces and waterbodies are largely absent. When the proportion of green roofs is implemented at scale, roofs that are only partly green can also create some extra cool islands (not merely normal islands) in high-density urban areas, equivalent to small green spaces and waterbodies. The sensitivity analysis of the cooling effect indicated that the maximum potential benefit of heat island reduction ranged from 4.04 km2 to 9.75 km2 when the coverage of green roofs was extended to the entire Xiamen Island. Besides, our results suggested that all proposed strategies would not remarkably moderate the thermal environment in the north of Xiamen Island, where urban planners should pay more attention in the future.

Shape-constrained convex regression problem deals with fitting a convex function to the observed data, where additional constraints are imposed, such as component-wise monotonicity and uniform Lipschitz continuity. This paper provides a comprehensive mechanism for computing the least squares estimator of a multivariate shape-constrained convex regression function in $\mathbb{R}^d$. We prove that the least squares estimator is computable via solving a constrained convex quadratic programming (QP) problem with $(n+1)d$ variables and at least $n(n-1)$ linear inequality constraints, where $n$ is the number of data points. For solving the generally very large-scale convex QP, we design two efficient algorithms, one is the symmetric Gauss-Seidel based alternating direction method of multipliers ({\tt sGS-ADMM}), and the other is the proximal augmented Lagrangian method ({\tt pALM}) with the subproblems solved by the semismooth Newton method ({\tt SSN}). Comprehensive numerical experiments, including those in the pricing of basket options and estimation of production functions in economics, demonstrate that both of our proposed algorithms outperform the state-of-the-art algorithm. The {\tt pALM} is more efficient than the {\tt sGS-ADMM} but the latter has the advantage of being simpler to implement.

Green roofs are thought to be an effective measure to solve the contradiction between land shortages and ecological construction, especially address urban heat island (UHI) effects in high-density urban areas. However, few empirical studies have focused on the cooling effect of green roof projects at urban scales. This study quantified the cooling effect of green roofs in Xiamen Island, China, where 540,000 m2 of green roofs were implemented between 2015 and 2017, in order to address the two research questions: (1) do green roofs in high-density urban areas have a significant cooling effect at the city scale and (2) what is the extent of the cooling? The relative difference between the average land surface temperature (LST) of Xiamen Island and the green roofs stemmed from Landsat 8 remote sensing image in the summers of 2014 and 2017 were calculated in geographic information systems (GIS) to represent the cooling effect of green roof project. Results showed that: (1) the average LST difference between green roofs and Xiamen Island decreased by 0.91 °C, indicating that green roofs could effectively alleviate UHI effects in high-density urban areas; (2) The cooling effect was significant up to 100 m from the green roof installation in Xiamen Island, we called it as characteristic cooling buffer zone; (3) Regression analysis revealed that for every 1000 m2 increase in green roof area, the average LST of the roof and its characteristic cooling buffer zone decreased by 0.4 °C. These findings provide the empirical proof for the cooling effect of green roofs on the surrounding environment in high-density urban areas and important insights for urban planners and government agencies for the effective mitigation of UHI impacts.

Peri-urban ecosystems are among the most intensive areas in terms of competition between different ecosystem components. Dissolved organic matter (DOM) plays a significant role in aquatic carbon cycling. The chemical composition of DOM and associated potential ecological risks in peri-urban aquatic ecosystems are poorly understood. Herein, we used fluorescence excitation-emission matrix and parallel factor analysis (EEM-PARAFAC) to characterize DOM in a peri-urban critical zone observatory watershed in Eastern China. According to the theory of natural disaster risk formation, we calculated the ecological risk of DOM in the peri-urban watershed. Seasonal variation in DOM concentrations was observed, whereas fluorescent DOM concentrations were site-specific across four sub-watersheds. The analysis of DOM absorption properties revealed the presence of DOM components with high aromatic content and large molecular weight in the watershed. Four fluorescent components (two humic-like and two protein-like substances) were identified using the PARAFAC model. Spatial distribution analysis showed that DOM quality was mainly influenced by human activities, and the proportion of protein-like substance (C3) was strongly correlated with anthropogenic parameters. The distribution of optical indices indicated diverse sources of DOM in the watershed. Ecological risk related to DOM was greater in the dry season than the wet season. There was a slight risk in most areas, with an extreme risk in areas experiencing the most intensive human disturbance, which were also extremely or heavily vulnerable. The results emphasize the strong influence of human disturbance on the ecological risk of DOM in peri-urban aquatic ecosystems. Our study provides useful information for ecological risk assessment of DOM that is difficult to obtain using traditional chemical analysis.

We focus on solving the clustered lasso problem, which is a least squares problem with the $\ell_1$-type penalties imposed on both the coefficients and their pairwise differences to learn the group structure of the regression parameters. Here we first reformulate the clustered lasso regularizer as a weighted ordered-lasso regularizer, which is essential in reducing the computational cost from $O(n^2)$ to $O(n\log (n))$. We then propose an inexact semismooth Newton augmented Lagrangian ({\sc Ssnal}) algorithm to solve the clustered lasso problem or its dual via this equivalent formulation, depending on whether the sample size is larger than the dimension of the features. An essential component of the {\sc Ssnal} algorithm is the computation of the generalized Jacobian of the proximal mapping of the clustered lasso regularizer. Based on the new formulation, we derive an efficient procedure for its computation. Comprehensive results on the global convergence and local linear convergence of the {\sc Ssnal} algorithm are established. For the purpose of exposition and comparison, we also summarize/design several first-order methods that can be used to solve the problem under consideration, but with the key improvement from the new formulation of the clustered lasso regularizer. As a demonstration of the applicability of our algorithms, numerical experiments on the clustered lasso problem are performed. The experiments show that the {\sc Ssnal} algorithm substantially outperforms the best alternative algorithm for the clustered lasso problem.

Residential spatial differentiation, also called residential segregation, is a representation of the differentiation of social stratum in economic income, social status, education degree, lifestyle, and other aspects, based on an urban geographical space. In this paper, Xiamen Island is taken as example to calculate the dissimilarity index and the multi-group dissimilarity index at three scales (districts, sub-districts, and communities) by using the land area, population size, and green space area of different housing types. The characteristics of residential differentiation are analyzed. It is found that both spatial differentiation and multi-group spatial differentiation have significant scale effects. The smaller the scale of the spatial statistics unit, the larger the spatial differentiation and multi-group spatial differentiation. Significant differences are found in residential differentiation among different housing types. The residential differentiation is, not only demonstrated in land area and population size, but also in the resources of green space. More importantly, a balanced allocation of green space will help to reduce the degree of residential differentiation. With urban expansion and social-economic development, residential spatial differentiation will likely change. An understanding of residential differentiation is a guide for urban master planning and detailed regulatory planning. It will help to promote social harmonious development and urban sustainable development by the reasonable configuration of land and resources.