Negative Convex Research Articles

Synergies and trade-offs of ecosystem services affected by land use structures of small watershed in the Loess Plateau

The Chinese government has implemented a series of ecological restoration projects in the Loess Plateau (LP), and the surface cover changed dramatically, impacting the ecosystem services (ESs) greatly. In this study, we used K-means clustering to classify the land use structures (LUSs) of the LP from 1990 to 2015 at the small watershed scale, and investigated the effects of LUS on water supply (WS), soil conservation (SC), and carbon sequestration (CS, expressed as NPP) with constraint lines. The values of WS and SC were obtained from the InVEST simulation, validated by the hydrographic station data. The results showed that the LUSs in LP were cropland structure (CLS, distinguished with CS), forest structure (FS), grassland structure (GS), crop-grassland structure (CGS), crop-forest-grassland structure (CFGS) and a very few areas of barren structure (BS). The proportion of dominant land use in those LUSs with a balance of WS, SC, and CS was 0.6–0.7 (cropland in CLS), 0.5 (forest in FS), 0.45/0.4 (cropland/grassland in CGS), 0.75 to 0.85 (grassland in GS), and 0.15/0.4/0.25 to 0.35 (cropland/forest/grassland in CFGS), respectively. The types of constraint curves of ESs for those LUSs involves hump-shaped curve, negative convex, half-concave-waved curve and concave-waved curve. This study proposed a method to objectively delineate LUS and improved the constraint line method to make it suitable for cases with less data, innovatively presenting the variation of ESs inside LUSs, which may provide a reference for optimal land planning and sustainable development of social-ecological systems.

Identifying the spatio-temporal pattern of drought characteristics and its constraint factors in the Yellow River Basin

The Yellow River Basin (YRB) constitutes an important grain-producing area, as well as an economic core area in China. However, drought and water shortage have always been important factors restricting the agricultural sustainable development of this region. The intensity of agricultural drought in the YRB and the factors affecting it need to be urgently clarified. Based on this, this study attempts to assess the spatio-temporal characteristics of agricultural drought in the YRB using the improved traditional temperature vegetation dryness index (ITVDI) and to identify the type and intensity of constraint effects of human activities (population, GDP, land use type), climate change (temperature, precipitation) and topography (elevation, slope) on drought in the YRB with the constraint line method. Results appeared that from 2001 to 2015, the drought intensity in the YRB exhibited fluctuating changes, while it decreased after 2015. Spatially, the drought characteristics of the YRB existed large heterogeneous, with drought showing a significant increase in the northwestern and downstream areas and a significant decrease in the central part of the basin. There were eight types of constraining effects of human activities, climate change, and topographic factors on drought intensity in the YRB, including U-shaped curve, positive linear, negative linear, logarithmic, negative convex, positive convex, exponential, and hump-shaped. Precipitation and temperature were the most direct factors affecting drought intensity and would exert a binding effect on both the upper and lower boundaries of drought intensity. The constraint effect of precipitation on drought varied in space. In the upstream and midstream, precipitation constrained the upper and lower boundaries of ITVDI, and the constraint effect increased with the increase of precipitation. In the downstream, the constraint effect of precipitation did not change significantly, and the maximum value of ITVDI was always less than 0.8. Temperature had upper and lower boundary constraint effects at three scales. The constraining effects of elevation, slope, GDP, and population were stable across scales. It should be noted that the constraint effect of land use type on drought exhibited U-shaped, and the threshold point of minimum values appeared in the areas covered by grassland and water. The constraint line method can improve the drought monitoring ability of ITVDI, as well as help to clarify the constraint factors and mechanism of drought intensity in the YRB and provide scientific decision-making support to mitigate regional drought and promote regional sustainable development.

Life satisfaction: The role of domain-specific reference points.

In the evaluation of well‐being, it is not only important what people have in absolute terms, but also how this compares to reference points in relative terms. We explore the relevance of relative comparisons by testing the effect of people's self‐rated position on potential reference points for income and health on their subjective well‐being. We used Multiple Discrepancies Theory as a framework to identify seven potentially relevant reference points for income and health. A representative sample (N = 550) of the Netherlands assessed their income and health relative to these reference points. In addition, we elicited monthly household income, health status (EQ‐5D‐5L), and subjective well‐being (SWLS). In line with the literature, we found a negative convex relationship between subjective well‐being and age and a positive relationship with being employed, income, and health. For income, subjective well‐being was also associated with how current income compared to respondents' needs and progression over time, and for health especially with how current health compared to what they felt they deserved. Our findings suggest that income and health are important for subjective well‐being both in absolute and relative terms. We found negative effects on life satisfaction if some of the domain specific reference points were not met.

Fertility transition and socioeconomic development in districts of India, 2001-2016.

The fertility-development relationship is bi-directional, context-specific, multi-phased and inconsistent over time. Indian districts provide an ideal setting to study this association due to their size, diversity and disparity in socioeconomic development. The objective of this study was to understand the association of fertility and socioeconomic development among the 640 districts of India. Data were drawn from multiple sources: Censuses of India 2001 and 2011; DLHS-2; NFHS-4; and other published sources. A district-level data file for Total Fertility Rate (TFR) and a set of developmental indices were prepared for the 640 districts for 2001 and 2016. Computation of a composite index (District Development Index, DDI), Ordinary Least Squares, Two Stage Least Squares and panel regressions were employed. By 2016, almost half of all Indian districts had attained below-replacement fertility, and 15% had a TFR of above 3.0. The DDI of India increased from 0.399 in 2001 to 0.511 by 2016 and showed large variations across districts. The correlation coefficient between TFR and DDI was -0.658 in 2001 and -0.640 in 2016. Districts with a DDI of between 0.3 and 0.6 in 2001 had experienced a fertility decline of more than 20%. The fertility-development relationship was found to be strongly negative, convex and consistent over time, but the level of association varied regionally. For any given level of DDI, fertility in 2016 was lower than in 2001; and the association was stronger in districts with a DDI below 0.45. The negative convex association between the two was prominent in the northern, central and eastern regions and the curves were flatter in the west, south and north-east. The increasing number of districts with low fertility and low development draws much attention. Some outlying districts in the north-eastern states had high TFR and high DDI (>0.6). Based on the findings, a multi-layered strategy in districts with low socioeconomic development is recommended. Additional investment in education, child health, employment generation and provisioning of contraceptives would improve the human development to achieve India's demographic goals.

Spatially explicit assessment of ecosystem services in China's Loess Plateau: Patterns, interactions, drivers, and implications

Abstract Human demands for natural resources have significantly changed the natural landscape and induced ecological degradation and associated ecosystem services. An understanding of the patterns, interactions, and drivers of ecosystem services is essential for the ecosystem management and guiding targeted land use policy-making. The Losses Plateau (LP) provides ecosystem services including the carbon sequestration and soil retention, and exerts tremendous impacts on the midstream and downstream of the Yellow River. Three dominant ecosystem services between 2000 and 2012 within the LP were presented based on multiple source datasets and biophysical models. In addition, paired ecosystem services interactions were quantified using the correlation analysis and constraint line approach. The main conclusions are as follows. It was observed that the warming and wetting climate and ecological program jointly promoted the vegetation growth and carbon sequestration. The increasing precipitation throughout 2000–2012 was related to the soil retention and hydrological regulation fluctuations. The vegetation restoration played a positive role in the soil retention enhancement, thus substantially reduced water and sediment yields. The relationships between ecosystem services were not only correlations (tradeoffs or synergies), but rather constraint effects. The constraint effects between the three paired ecosystem services could be classified as the negative convex (carbon sequestration vs. hydrological regulation) and hump-shaped (soil retention vs. carbon sequestration and soil retention vs. hydrological regulation), and the coefficients of determination for the entire LP were 0.78, 0.84, and 0.65, respectively. In the LP, the rainfall (water availability) was the key constraint factor that affected the relationships between the paired ecosystem services. The spatially explicit mapping of ecosystem services and interaction analyses utilizing constraint line approach enriched the understanding of connections between ecosystem services and the potential drivers, which had important implications for the land use planning and landscapes services optimizing.

Relationship between paired ecosystem services in the grassland and agro-pastoral transitional zone of China using the constraint line method

Understanding the relationships between ecosystem services is important for promoting ecosystem service management and sustainable development. The relationships between ecosystem services have commonly been characterized as tradeoffs and synergies. Here, we report that a third type of relationship also exists, in which one ecosystem service constrains the other. Selecting the grassland and agro-pastoral transitional zone of North China (GAPTZ) as the study area, we examined the relationships between paired ecosystem services: net primary productivity (NPP), soil conservation (SC), soil erosion by wind (SL), water yield (WY), and water retention (WR). The constraint effect of one ecosystem service on the other was determined by extracting the upper constraint lines from the scatter plots of the paired ecosystem services with segmented quantile regression on the levels of landscape, class, and ecoregion. Our results revealed eight types of constraint effects between the ten paired ecosystem services: (1) positive linear, (2) negative linear, (3) logarithmic, (4) negative convex, (5) backward S-shaped, (6) hump-shaped, (7) convex-waved, and (8) concave-waved. At the landscape, class, and ecoregion levels, there was a hump-shaped constraint effect between NPP and SC. Precipitation was the main factor shaping the constraint line of the paired NPP-SC. The gradually increasing constraint effect of higher NPP on WY indicated that, in arid and semiarid areas, improving NPP decreases water yield. In farmland areas, the backward S-shaped constraint line of the paired NPP-SL indicates that crops, unlike forests and grasslands, could not protect soil from wind erosion. The constraint effects of SL on WY and WR are negative convex on the landscape level and convex-waved or concave-waved on the class and ecoregion levels. The constraint line approach enriches the understanding of linkages between ecosystem services and the potential drivers. The constraint effects of ecosystem services have important implications for sustainable land use planning to optimize landscapes services.

Prescribing curvature problems on the Bakry-Emery Ricci tensor of a compact manifold with boundary

The authors consider the problem of conformally deforming a metric such that the k-curvature defined by an elementary symmetric function of the eigenvalues of the Bakry-Emery Ricci tensor on a compact manifold with boundary to a prescribed function. A consequence of our main result is that there exists a complete metric such that the Monge-Ampere type equation with respect to its Bakry-Emery Ricci tensor is solvable, provided that the initial Bakry-Emery Ricci tensor belongs to a negative convex cone.

An Algorithm for Unconstrained Quadratically Penalized Convex Optimization

Estimators are often defined as the solutions to data dependent optimization problems. A common form of objective function (function to be optimized) that arises in statistical estimation is the sum of a convex function V and a quadratic complexity penalty. A standard paradigm for creating kernel-based estimators leads to such an optimization problem. This article describes an optimization algorithm designed for unconstrained optimization problems in which the objective function is the sum of a non negative convex function and a known quadratic penalty. The algorithm is described and compared with BFGS on some penalized logistic regression and penalized L 3/2 regression problems.

Extinction vulnerability of coral reef fishes

With rapidly increasing rates of contemporary extinction, predicting extinction vulnerability and identifying how multiple stressors drive non-random species loss have become key challenges in ecology. These assessments are crucial for avoiding the loss of key functional groups that sustain ecosystem processes and services. We developed a novel predictive framework of species extinction vulnerability and applied it to coral reef fishes. Although relatively few coral reef fishes are at risk of global extinction from climate disturbances, a negative convex relationship between fish species locally vulnerable to climate change vs. fisheries exploitation indicates that the entire community is vulnerable on the many reefs where both stressors co-occur. Fishes involved in maintaining key ecosystem functions are more at risk from fishing than climate disturbances. This finding is encouraging as local and regional commitment to fisheries management action can maintain reef ecosystem functions pending progress towards the more complex global problem of stabilizing the climate.

Complete Conformal Metrics of Negative Ricci Curvature on Compact Manifolds with Boundary

We study the problem of finding complete conformal metrics determined by a symmetric function of Ricci tensor in a negative convex cone on compact manifolds. A consequence of our main results is that any smooth bounded domain in Euclidean space of dimension greater or equal to 3 admits a complete conformally flat metric of negative Ricci curvature with .

Singular boundary value problems for the Monge–Ampère equation

Given a strictly convex, smooth, and bounded domain Ω in R n we consider solving the Monge–Ampére equation det ( D 2 u ) = f ( x , − u ) for solutions in C ∞ ( Ω ) ∩ C ( Ω ¯ ) with zero boundary value, where the nonlinearity f ( x , t ) could be singular at t = 0 . We will show that under some fairly general assumptions on f the above Dirichlet problem admits a negative convex solution in Ω . Uniqueness of such solutions is then established for a wide class of nonlinearities f ( x , t ) as a consequence of a comparison principle.

Existence and estimates of solutions to a singular Dirichlet problem for the Monge–Ampère equation

Given a strictly convex, smooth, and bounded domain Ω in R n we establish the existence of a negative convex solution in C ∞ ( Ω ) ∩ C ( Ω ¯ ) with zero boundary value to the singular Monge–Ampère equation det ( D 2 u ) = p ( x ) g ( − u ) . An associated Dirichlet problem will be employed to provide a necessary and sufficient condition for the solvability of the singular boundary value problem. Estimates of solutions will also be given and regularity of solutions will be deduced from the estimates.

多面体の類似度の定量化に関する研究 （第１報） 凸分解を利用した新しいデータ構造の提案とその生成アルゴリズムについて

As a basis for treating geometrical similarities of 3-D objects, an idea of a new data structure called layer structure with convex for representing polyhedra is presented. The two layer structure, which can be constructed uniquely for a polyhedron, consists of convex components separated into two layers, i.e., the first layer includes only positive convex components to be added and the second layer represents negative convex components to be subtracted from positive ones. The procedure for constructing the two layer structure consists of the following two processes. (1) Forward process: A concave polyhedron is decomposed and represented as a hierarchical tree structure with convex components. (2) Backward process: Components belonging to leaf nodes of the tree structure are put into the two layer structure according to the level of the node. The components are removed from the original polyhedron after processing each leaf node of the tree structure. These procedures are repeated to the modified object until the processes reach to the root node. The two layer structure can be applied for extracting features of polyhedra such as protrusions, holes and pockets, and comparing 3-D objects.

Ratio prophet inequalities for convex functions of partial sums

Let x,, x,,... be independent mean zero random variables and set S, =X, + . * * +X,, and S,* = maxi ~ k ~ ,,S: . We are interested in comparing Sz and S,* for large values of their ranges. Since we cannot compare their tail probabilities directly, we compare ENS,*) with E@(Sz), where @ is any non-decreasing non negative convex function on [O, m). For the convex functions Q,(x) = I x I ‘, square function inequalities are known to become proportionately worse and worse as P + 00. (See Hitczenko (1990) for a summary of what is known.) It may therefore seem surprising that for all @, n and Xi,. . . , X,,, E@(S,*) , Y) (3) for all y sufficiently large (perhaps depending on IZ and Xi, . . . , X,). This inequality is trivial if the variates are symmetric. But even in the i.i.d. case it is essentially false, as shown by B. Davis (for n = 2). To see this, let X, and X, be i.i.d. mean zero random variables with P(X, 'Y) = & and P(X,= -:)=A.

Convex molecule perturbation theory for the gaussian overlap system

Perturbation theory of convex molecules is reformulated to describe the equilibrium behaviour of axisymmetric molecules interacting via the gaussian overlap potential and employed to describe the equilibrium behaviour of three systems (with κ = 0·5, 1·3 and 1·55) at several temperatures. To get parameters of the corresponding Kihara pair potential (with the negative parallel convex body to the given ellipsoid as a core) the condition of the equal values of the second virial coefficients is used. The calculated values of the residual Helmholtz free energy, residual internal energy and compressibility factor compare well with recent simulation data.