Defining Urban Boundaries by Characteristic Scales

Defining an objective boundary for a city is a difficult problem, which remains to be solved by an effective method. Recent years, new methods for identifying urban boundary have been developed by means of spatial search techniques (e.g. CCA). However, the new algorithms are involved with another problem, that is, how to determine the characteristic radius of spatial search. This paper proposes new approaches to looking for the most advisable spatial searching radius for determining urban boundary. We found that the relationships between the spatial searching radius and the corresponding number of clusters take on an exponential function. In the exponential model, the scale parameter just represents the characteristic length that we can use to define the most objective urban boundary objectively. Two sets of China's cities are employed to test this method, and the results lend support to the judgment that the characteristic parameter can well serve for the spatial searching radius. The research may be revealing for making urban spatial analysis in methodology and implementing identification of urban boundaries in practice.Comment: 26 pages, 5 figures, 7 table

Measure upper bounds of nodal sets of solutions to Dirichlet problem of Schr\"{o}dinger equations

In this paper, we focus on estimating measure upper bounds of nodal sets of solutions to the following boundary value problem \begin{equation*} \left\{ \begin{array}{lll} \Delta u+Vu=0\quad \mbox{in}\ \Omega,\\[2mm] u=0\quad \mbox{on}\ \partial\Omega, \end{array}\right. \end{equation*} where $V\in W^{1,\infty}(\Omega)$ is a potential and $\Omega\subset \mathbb{R}^n (n\geq2)$ is a bounded domain. We show that upper bounds on the $(n-1)$-dimensional Hausdorff measure of the nodal sets of $u$ in $\Omega$ is less than or equal to $$C\Big(1+\log\left(\|\nabla V\|_{L^{\infty}(\Omega)}+1\right)\Big)\cdot\left(\|V\|_{L^{\infty}(\Omega)}^{\frac{1}{2}}+|\nabla V\|_{L^{\infty}(\Omega)}^{\frac{1}{2}}+1\right),$$ provided $\partial\Omega$ is $C^{2}$-smooth and $V$ is analytic. Here $C$ is a positive constant depending only on $n$ and $\Omega$. In particular, if $\|\nabla V\|_{L^{\infty}(\Omega)}$ is small, the measure upper bound of the of nodal set of $u$ is less than or equal to $C\left(\|V\|^{\frac{1}{2}}_{L^{\infty}(\Omega)}+1\right)$.Comment: 35page

Quantitative unique continuation property for solutions to a bi-Laplacian equation with a potential

In this paper, we focus on the quantitative unique continuation property of solutions to \begin{equation*} \Delta^2u=Vu, \end{equation*} where $V\in W^{1,\infty}$. We show that the maximal vanishing order of the solutions is not large than \begin{equation} C\left(\|V\|^{\frac{1}{4}}_{L^{\infty}}+\|\nabla V\|_{L^{\infty}}+1\right). \end{equation} Our key argument is to lift the original equation to that with a positive potential, then decompose the resulted fourth-order equation into a special system of two second-order equations. Based on the special system, we define a variant frequency function with weights and derive its almost monotonicity to establishing some doubling inequalities with explicit dependence on the Sobolev norm of the potential function.Comment: 21page

Idle block based methods for cloud workflow scheduling with preemptive and non-preemptive tasks

[EN] Complex workflow applications are widely used in scientific computing and economic analysis, which commonly include both preemptive and non-preemptive tasks. Cloud computing provides a convenient way for users to access different resources based on the ¿pay-as-you-go¿ model. However, different resource renting alternatives (reserved, on-demand or spot) are usually provided by the service provider. The spot instances provide a dynamic and cheaper alternative comparing to the on-demand one. However, failures often occur due to the fluctuations of the price of the instance. It is a big challenge to determine the appropriate amount of spot and on-demand resources for workflow applications with both preemptive and non-preemptive tasks. In this paper, the workflow scheduling problem with both spot and on-demand instances is considered. The objective is to minimize the total renting cost under deadline constrains. An idle time block-based method is proposed for the considered problem. Different idle time block-based searing and improving strategies are developed to construct schedules for workflow applications. Schedules are improved by a forward and backward moving mechanism. Experimental and statistical results demonstrate the effectiveness of the proposed algorithm over a lot of tests with different sizes.This work is supported by the National Natural Science Foundation of China (No. 61572127, 61272377), the National Key Research and Development Program of China (No. 2017YFB1400800). Ruben Ruiz is partially supported by the Spanish Ministry of Economy and Competitiveness, under the project "SCHEYARD - Optimization of Scheduling Problems in Container Yards" (No. DPI2015-65895-R) financed by FEDER funds.Chen, L.; Li, X.; Ruiz García, R. (2018). Idle block based methods for cloud workflow scheduling with preemptive and non-preemptive tasks. Future Generation Computer Systems. 89:659-669. https://doi.org/10.1016/j.future.2018.07.037S6596698

Resource Renting for Periodical Cloud Workflow Applications

[EN] Cloud computing is a new resource provisioning mechanism, which represents a convenient way for users to access different computing resources. Periodical workflow applications commonly exist in scientific and business analysis, among many other fields. One of the most challenging problems is to determine the right amount of resources for multiple periodical workflow applications. In this paper, the periodical workflow applications scheduling problem with total renting cost minimization is considered. The novelty of this work relies precisely on this objective function, which is more realistic in practice than the more commonly considered makespan minimization. An integer programming model is constructed for the problem under study. A Precedence Tree based Heuristic (PTH) is developed which considers three types of initial schedule construction methods. Based on the initial schedule, two improvement procedures are presented. The proposed methods are compared with existing algorithms for the related makespan based multiple workflow scheduling problem. Experimental and statistical results demonstrate the effectiveness and efficiency of the proposed algorithm.This work is supported by the National Natural Science Foundation of China (No. 61572127, 61272377), the Key Research & Development program in Jiangsu Province (No. BE2015728) and Collaborative Innovation Center of Wireless Communications Technology. Ruben Ruiz is partially supported by the Spanish Ministry of Economy and Competitiveness, under the project "SCHEYARD-Optimization of Scheduling Problems in Container Yards" (No. DPI2015-65895-R) financed by FEDER funds.Chen, L.; Li, X.; Ruiz García, R. (2020). Resource Renting for Periodical Cloud Workflow Applications. IEEE Transactions on Services Computing. 13(1):130-143. https://doi.org/10.1109/TSC.2017.2677450S13014313

Trajectory Scheduling Methods for minimizing total tardiness in a flowshop

AbstractIn this paper, Trajectory Scheduling Methods (TSMs) are proposed for the permutation flowshop scheduling problem with total tardiness minimization criterion. TSMs belong to an iterative local search framework, in which local search is performed on an initial solution, a perturbation operator is deployed to improve diversification, and a restart point mechanism is used to select the new start point of another cycle. In terms of the insertion and swap neighborhood structures, six composite heuristics are introduced, which exploit the search space with a strong intensification effect. Based on purely insertion-based or swap-based perturbation structures, three compound perturbation structures are developed that construct a candidate restart point set rather than just a single restart point. The distance between the current best solution and each start point of the set is defined, according to which the diversification effect of TSMs can be boosted by choosing the most appropriate restart point for the next iteration. A total of 18 trajectory scheduling methods are constructed by different combinations of composite heuristics. Both the best and worst combinations are compared with three best existing sequential meta-heuristics for the considered problem on 540 benchmark instances. Experimental results show that the proposed heuristics significantly outperform the three best existing algorithms within the same computation time

Hybrid resource provisioning for cloud workflows with malleable and rigid tasks

[EN] In cloud computing, reserved and on-demand instances are generally provided by service providers. Hybridization of the two alternatives can considerably save costs when renting resources from the cloud. However, it is a big challenge to determine the appropriate amount of reserved and on-demand resources in terms of users' requirements. In this paper, the workflow scheduling problem with both reserved and on-demand instances is considered. The objective is to minimize the total rental cost under deadline constrains. The considered problem is mathematically modeled. A multiple sequence-based earliest finish time method is proposed to construct schedules for the workflows. Four different rules are used to generate initial task allocation sequences. Types and quantities of resources are determined by a free time block-based schedule construction mechanism. New sequences are generated by a variable neighborhood search method. Experimental and statistical analyses and results demonstrate that the proposed algorithm algorithm generates considerable cost savings when compared to the algorithms with only on-demand or reserved instances.l This work is supported by the National Key Research and Development Program of China (No. 2017YFB1400801), the National Natural Science Foundation of China (Nos. 61572127, 61872077, 61832004) and Collaborative Innovation Center of Wireless Communications Technology. Rub~en Ruiz is supported by the Spanish Ministry of Economy and Competitiveness, under the project "SCHEYARD-Optimization of scheduling problems in container yards" (No. DPI2015-65895-R) partly financed with FEDER funds.Chen, L.; Li, X.; Guo, Y.; Ruiz García, R. (2021). Hybrid resource provisioning for cloud workflows with malleable and rigid tasks. IEEE Transactions on Cloud Computing. 9(3):1089-1102. https://doi.org/10.1109/TCC.2019.2894836S108911029

FOREARC MANTLE METASOMATISM BY 11B-DEPLETED FLUIDS FROM A HIGHLY DEHYDRATED SLAB: A SNAPSHOT OF SLAB ROLL-BACK?

Accretionary orogens form along convergent plate margins due to the ongoing subduction of oceanic lithosphere, and comprise accretionary prisms, magmatic arcs, back-arc domains, ophiolitic mélanges and possibly oceanic plateaus and continental fragments [Condie, 2007; Cawood et al., 2009]. Based on the dips and velocities of subducting slabs, accretionary orogens can be divided into retreating and advancing type, as exemplified by modern SW Pacific and Andes, respectively [Royden, 1993; Cawood et al., 2009].Accretionary orogens form along convergent plate margins due to the ongoing subduction of oceanic lithosphere, and comprise accretionary prisms, magmatic arcs, back-arc domains, ophiolitic mélanges and possibly oceanic plateaus and continental fragments [Condie, 2007; Cawood et al., 2009]. Based on the dips and velocities of subducting slabs, accretionary orogens can be divided into retreating and advancing type, as exemplified by modern SW Pacific and Andes, respectively [Royden, 1993; Cawood et al., 2009]