Surface and borehole gravity data contain complementary information.Thus,the joint inversion of these two data types can help retrieve the real spatial distributions of density bodies.When a sharp boundary exists betw...Surface and borehole gravity data contain complementary information.Thus,the joint inversion of these two data types can help retrieve the real spatial distributions of density bodies.When a sharp boundary exists between an anomalous density body and its surrounding rock,the interface recovered by smooth inversion with Tikhonov regularization is not clear,leading to difficulties in the subsequent geological interpretation.In this work,we develop a joint inversion of surface and borehole gravity data using zeroth-order minimum entropy regularization.The method takes advantage of the complementary information from surface and borehole gravity data to enhance the imaging resolution of density bodies.It also produces a focused imaging of bodies through the zeroth-order minimum entropy regularization without requiring a preselection of a proper focusing parameter.We apply the developed joint inversion approach to three diff erent synthetic data sets.Inversion results show that the focusing inversion with the zeroth-order minimum entropy regularization provides a good description of the true spatial extent of anomalous density bodies.Meanwhile,the joint focusing inversion reconstructs a more reliable density model with a relatively high resolution when a density body is passed through by one or more boreholes.展开更多
This paper proposes a tunable zeroth-order resonator on a composite right/left-handed transmission line consisting of a transversely magnetized ferrite substrate periodically loaded by microstrip inductors. Based on t...This paper proposes a tunable zeroth-order resonator on a composite right/left-handed transmission line consisting of a transversely magnetized ferrite substrate periodically loaded by microstrip inductors. Based on the propagation theory of edge guided modes, the analysis procedure of this structure is introduced. The numerical results demonstrate the tunability of the resonant frequency by changing the DC bias magnetic field applied to the ferrite. In contrast to previous work, the proposed structure is easy to design and fabricate and does not require a chip component.展开更多
A formula was proved for computing the zeroth-order general Randic index of a hexagonal system to explore the correlation between the zeroth-order general Randic index and the π-electronic energy of a hexagonal syste...A formula was proved for computing the zeroth-order general Randic index of a hexagonal system to explore the correlation between the zeroth-order general Randic index and the π-electronic energy of a hexagonal system.As a consequence,the extremal hexagonal systems with minimum or maximum zeroth-order general Randic index were completely characterized.Moreover,by using the least-square fit method and regression analysis,a new and close relation was found between the zeroth-order general Randic index and the π-electronic energy of a hexagonal system.So the zeroth-order general Randic index is a good measure of the π-electronic energies for benzenoid hydrocarbons.展开更多
Let G be a connected graph with order n,minimum degree δ = δ（G） and edge-connectivity λ =λ（G）. A graph G is maximally edge-connected if λ = δ, and super edge-connected if every minimum edgecut consists of ed...Let G be a connected graph with order n,minimum degree δ = δ（G） and edge-connectivity λ =λ（G）. A graph G is maximally edge-connected if λ = δ, and super edge-connected if every minimum edgecut consists of edges incident with a vertex of minimum degree. Define the zeroth-order general Randic index R_α-0（G） =Σ x∈V（G） d_G-α（x）, where dG（x） denotes the degree of the vertex x. In this paper, we present two sufficient conditions for graphs and triangle-free graphs to be super edge-connected in terms of the zeroth-order general Randic index for -1 ≤α 〈 0, respectively.展开更多
Define the zeroth-order Randic index R^(0)(G)=∑x∈V(G)1/√dG1(x),where dG(x)denotes the degree of the vertex x.In this paper,we present two sufficient conditions for graphs and triangle-free graphs to be super-edge-c...Define the zeroth-order Randic index R^(0)(G)=∑x∈V(G)1/√dG1(x),where dG(x)denotes the degree of the vertex x.In this paper,we present two sufficient conditions for graphs and triangle-free graphs to be super-edge-connected in terms of the zeroth-order Randic index,respectively.展开更多
This paper introduces dynamic mode decomposition(DMD)as a novel approach to model the breakage kinetics of particulate systems.DMD provides a data-driven framework to identify a best-fit linear dynamics model from a s...This paper introduces dynamic mode decomposition(DMD)as a novel approach to model the breakage kinetics of particulate systems.DMD provides a data-driven framework to identify a best-fit linear dynamics model from a sequence of system measurement snapshots,bypassing the nontrivial task of determining appropriate mathemat-ical forms for the breakage kernel functions.A key innovation of our method is the instilling of physics-informed constraints into the DMD eigenmodes and eigenvalues,ensuring they adhere to the physical structure of particle breakage processes even under sparse measurement data.The integration of eigen-constraints is computationally aided by a zeroth-order global optimizer for solving the nonlinear,nonconvex optimization problem that elicits system dynamics from data.Our method is evaluated against the state-of-the-art optimized DMD algorithm using both generated data and real-world data of a batch grinding mill,showcasing over an order of magnitude lower prediction errors in data reconstruction and forecasting.展开更多
This paper investigates a class of constrained distributed zeroth-order optimization(ZOO) problems over timevarying unbalanced graphs while ensuring privacy preservation among individual agents. Not taking into accoun...This paper investigates a class of constrained distributed zeroth-order optimization(ZOO) problems over timevarying unbalanced graphs while ensuring privacy preservation among individual agents. Not taking into account recent progress and addressing these concerns separately, there remains a lack of solutions offering theoretical guarantees for both privacy protection and constrained ZOO over time-varying unbalanced graphs.We hereby propose a novel algorithm, termed the differential privacy(DP) distributed push-sum based zeroth-order constrained optimization algorithm(DP-ZOCOA). Operating over time-varying unbalanced graphs, DP-ZOCOA obviates the need for supplemental suboptimization problem computations, thereby reducing overhead in comparison to distributed primary-dual methods. DP-ZOCOA is specifically tailored to tackle constrained ZOO problems over time-varying unbalanced graphs,offering a guarantee of convergence to the optimal solution while robustly preserving privacy. Moreover, we provide rigorous proofs of convergence and privacy for DP-ZOCOA, underscoring its efficacy in attaining optimal convergence without constraints. To enhance its applicability, we incorporate DP-ZOCOA into the federated learning framework and formulate a decentralized zeroth-order constrained federated learning algorithm(ZOCOA-FL) to address challenges stemming from the timevarying imbalance of communication topology. Finally, the performance and effectiveness of the proposed algorithms are thoroughly evaluated through simulations on distributed least squares(DLS) and decentralized federated learning(DFL) tasks.展开更多
基金financially supported by the National Key Research and Development Program of China(no.2018YFC0603300)the National Natural Science Foundation of China(no.42004054)。
文摘Surface and borehole gravity data contain complementary information.Thus,the joint inversion of these two data types can help retrieve the real spatial distributions of density bodies.When a sharp boundary exists between an anomalous density body and its surrounding rock,the interface recovered by smooth inversion with Tikhonov regularization is not clear,leading to difficulties in the subsequent geological interpretation.In this work,we develop a joint inversion of surface and borehole gravity data using zeroth-order minimum entropy regularization.The method takes advantage of the complementary information from surface and borehole gravity data to enhance the imaging resolution of density bodies.It also produces a focused imaging of bodies through the zeroth-order minimum entropy regularization without requiring a preselection of a proper focusing parameter.We apply the developed joint inversion approach to three diff erent synthetic data sets.Inversion results show that the focusing inversion with the zeroth-order minimum entropy regularization provides a good description of the true spatial extent of anomalous density bodies.Meanwhile,the joint focusing inversion reconstructs a more reliable density model with a relatively high resolution when a density body is passed through by one or more boreholes.
文摘This paper proposes a tunable zeroth-order resonator on a composite right/left-handed transmission line consisting of a transversely magnetized ferrite substrate periodically loaded by microstrip inductors. Based on the propagation theory of edge guided modes, the analysis procedure of this structure is introduced. The numerical results demonstrate the tunability of the resonant frequency by changing the DC bias magnetic field applied to the ferrite. In contrast to previous work, the proposed structure is easy to design and fabricate and does not require a chip component.
基金National Natural Science Foundation of China (No. 10901034)Chenguang Program of Shanghai Education Development Foundation,China (No. 2008CG40)
文摘A formula was proved for computing the zeroth-order general Randic index of a hexagonal system to explore the correlation between the zeroth-order general Randic index and the π-electronic energy of a hexagonal system.As a consequence,the extremal hexagonal systems with minimum or maximum zeroth-order general Randic index were completely characterized.Moreover,by using the least-square fit method and regression analysis,a new and close relation was found between the zeroth-order general Randic index and the π-electronic energy of a hexagonal system.So the zeroth-order general Randic index is a good measure of the π-electronic energies for benzenoid hydrocarbons.
基金supported by the National Natural Science Foundation of China(No.11501490,61373019,11371307)by the Natural Science Foundation of Shandong Province(No.ZR2015AM006)
文摘Let G be a connected graph with order n,minimum degree δ = δ（G） and edge-connectivity λ =λ（G）. A graph G is maximally edge-connected if λ = δ, and super edge-connected if every minimum edgecut consists of edges incident with a vertex of minimum degree. Define the zeroth-order general Randic index R_α-0（G） =Σ x∈V（G） d_G-α（x）, where dG（x） denotes the degree of the vertex x. In this paper, we present two sufficient conditions for graphs and triangle-free graphs to be super edge-connected in terms of the zeroth-order general Randic index for -1 ≤α 〈 0, respectively.
基金This work is supported by the National Natural Science Foundation of China(Nos.11501490,61373019,13071107)the Natural Science Foundation of Shandong Province(No.ZR2015AM006).
文摘Define the zeroth-order Randic index R^(0)(G)=∑x∈V(G)1/√dG1(x),where dG(x)denotes the degree of the vertex x.In this paper,we present two sufficient conditions for graphs and triangle-free graphs to be super-edge-connected in terms of the zeroth-order Randic index,respectively.
基金supported by the Ramanujan Fellowship from the Science and Engineering Research Board,Government of India(Grant No.RJF/2022/000115).
文摘This paper introduces dynamic mode decomposition(DMD)as a novel approach to model the breakage kinetics of particulate systems.DMD provides a data-driven framework to identify a best-fit linear dynamics model from a sequence of system measurement snapshots,bypassing the nontrivial task of determining appropriate mathemat-ical forms for the breakage kernel functions.A key innovation of our method is the instilling of physics-informed constraints into the DMD eigenmodes and eigenvalues,ensuring they adhere to the physical structure of particle breakage processes even under sparse measurement data.The integration of eigen-constraints is computationally aided by a zeroth-order global optimizer for solving the nonlinear,nonconvex optimization problem that elicits system dynamics from data.Our method is evaluated against the state-of-the-art optimized DMD algorithm using both generated data and real-world data of a batch grinding mill,showcasing over an order of magnitude lower prediction errors in data reconstruction and forecasting.
基金supported in part by the National Key Research and Development Program of China(2022ZD0120001)the National Natural Science Foundation of China(62233004,62273090,62073076)the Jiangsu Provincial Scientific Research Center of Applied Mathematics(BK20233002)
文摘This paper investigates a class of constrained distributed zeroth-order optimization(ZOO) problems over timevarying unbalanced graphs while ensuring privacy preservation among individual agents. Not taking into account recent progress and addressing these concerns separately, there remains a lack of solutions offering theoretical guarantees for both privacy protection and constrained ZOO over time-varying unbalanced graphs.We hereby propose a novel algorithm, termed the differential privacy(DP) distributed push-sum based zeroth-order constrained optimization algorithm(DP-ZOCOA). Operating over time-varying unbalanced graphs, DP-ZOCOA obviates the need for supplemental suboptimization problem computations, thereby reducing overhead in comparison to distributed primary-dual methods. DP-ZOCOA is specifically tailored to tackle constrained ZOO problems over time-varying unbalanced graphs,offering a guarantee of convergence to the optimal solution while robustly preserving privacy. Moreover, we provide rigorous proofs of convergence and privacy for DP-ZOCOA, underscoring its efficacy in attaining optimal convergence without constraints. To enhance its applicability, we incorporate DP-ZOCOA into the federated learning framework and formulate a decentralized zeroth-order constrained federated learning algorithm(ZOCOA-FL) to address challenges stemming from the timevarying imbalance of communication topology. Finally, the performance and effectiveness of the proposed algorithms are thoroughly evaluated through simulations on distributed least squares(DLS) and decentralized federated learning(DFL) tasks.
