Pub Date : 2025-04-26DOI: 10.1007/s10878-025-01291-6
Brian Godwin Lim, Renzo Roel Tan, Richard de Jesus, Lessandro Estelito Garciano, Agnes Garciano, Kazushi Ikeda
Lifeline utility networks have been studied extensively within the domain of network reliability due to the prevalence of natural hazards. The reliability of these networks is typically investigated through graphs that retain their structural characteristics. This paper introduces novel connectivity-based reliability measures tailored for stochastic graphs with designated source vertices and failure-probability-weighted edges. In particular, the per-vertex path survival reliability quantifies the average survival likelihood of single-source paths from a vertex to any source. A consolidated per-graph reliability measure is also presented, incorporating graph density and the shortest distance to a source as regulating elements for network comparison. To highlight the advantages of the proposed reliability measures, a theoretical discussion of their key properties is presented, along with a comparison against standard reliability measurements. The proposal is further accompanied by an efficient calculation procedure utilizing the zero-suppressed binary decision diagram, constructed through the frontier-based search, to compactly represent all single-source paths. Finally, the path survival reliabilities are calculated for a set of real-world networks and demonstrated to provide practical insights.
{"title":"Path survival reliabilities as measures of reliability for lifeline utility networks","authors":"Brian Godwin Lim, Renzo Roel Tan, Richard de Jesus, Lessandro Estelito Garciano, Agnes Garciano, Kazushi Ikeda","doi":"10.1007/s10878-025-01291-6","DOIUrl":"https://doi.org/10.1007/s10878-025-01291-6","url":null,"abstract":"<p>Lifeline utility networks have been studied extensively within the domain of network reliability due to the prevalence of natural hazards. The reliability of these networks is typically investigated through graphs that retain their structural characteristics. This paper introduces novel connectivity-based reliability measures tailored for stochastic graphs with designated source vertices and failure-probability-weighted edges. In particular, the per-vertex path survival reliability quantifies the average survival likelihood of single-source paths from a vertex to any source. A consolidated per-graph reliability measure is also presented, incorporating graph density and the shortest distance to a source as regulating elements for network comparison. To highlight the advantages of the proposed reliability measures, a theoretical discussion of their key properties is presented, along with a comparison against standard reliability measurements. The proposal is further accompanied by an efficient calculation procedure utilizing the zero-suppressed binary decision diagram, constructed through the frontier-based search, to compactly represent all single-source paths. Finally, the path survival reliabilities are calculated for a set of real-world networks and demonstrated to provide practical insights.\u0000</p>","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"16 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143876097","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-04-26DOI: 10.1016/j.chaos.2025.116433
Victoria Arcón, Inés Caridi
This paper proposes metrics to characterize and quantify the spatial scale of ethnic-based residential segregation using random walkers on city networks built from census data. We analyze the diversity of encounters experienced by the walkers over time. We provide a probabilistic framework and numerical methods to compute the probability of encountering a certain number of ethnic groups at each time, and use it to define two indices: the homogeneity scope, which represents the time when it becomes more likely or expected to leave the homogeneous area of the starting ethnic group, and the complete diversity scope, the time when it becomes more likely or expected to encounter all ethnic groups. These indices are also generalized to reach specific intermediate levels of diversity. We apply the methodology to lattice toy models and a case study in Rio de Janeiro. Our approach identifies areas and groups of high homogeneity, highlighting opportunities to enhance social interaction through improved connectivity. The proposed framework can be adapted for alternative definitions of city networks, broadening its applicability to various research interests.
{"title":"Homogenization scales in residential segregation through random walkers","authors":"Victoria Arcón, Inés Caridi","doi":"10.1016/j.chaos.2025.116433","DOIUrl":"10.1016/j.chaos.2025.116433","url":null,"abstract":"<div><div>This paper proposes metrics to characterize and quantify the spatial scale of ethnic-based residential segregation using random walkers on city networks built from census data. We analyze the diversity of encounters experienced by the walkers over time. We provide a probabilistic framework and numerical methods to compute the probability of encountering a certain number of ethnic groups at each time, and use it to define two indices: the homogeneity scope, which represents the time when it becomes more likely or expected to leave the homogeneous area of the starting ethnic group, and the complete diversity scope, the time when it becomes more likely or expected to encounter all ethnic groups. These indices are also generalized to reach specific intermediate levels of diversity. We apply the methodology to lattice toy models and a case study in Rio de Janeiro. Our approach identifies areas and groups of high homogeneity, highlighting opportunities to enhance social interaction through improved connectivity. The proposed framework can be adapted for alternative definitions of city networks, broadening its applicability to various research interests.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"197 ","pages":"Article 116433"},"PeriodicalIF":5.3,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143873825","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Neuromorphic computing has garnered significant attention for its ability to emulate biological neural networks, yet challenges remain in simulating the behavioral dynamics and constructing the structural frameworks of neural synapses. This paper examines the neuromorphic dynamics and synchronization of fractional-order memristive systems, highlighting their potential as artificial synapses in neuromorphic computing. A 3-D fractional-order circuit was developed based on mathematical modeling of locally active memristors, revealing diverse neurodynamic behaviors, including action potentials, oscillations, and spike bursting, under varying fractional-order indices and parameters. The fractional-order boundaries for neuromorphic behaviors were discussed, and dynamic variations across different initial conditions were analyzed. A fractional-order finite-time synchronization controller was designed to achieve effective behavioral synchronization between independent memristive synapses. These findings offer valuable insights into the dynamic complexity of fractional-order systems, paving the way for their application in the design of neuromorphic systems and artificial neural networks.
{"title":"Neuromorphic dynamics and behavior synchronization of fractional-order memristive synapses","authors":"Yukaichen Yang, Xiang Xu, Gangquan Si, Minglin Xu, Chenhao Li, Ruicheng Xie","doi":"10.1016/j.chaos.2025.116469","DOIUrl":"10.1016/j.chaos.2025.116469","url":null,"abstract":"<div><div>Neuromorphic computing has garnered significant attention for its ability to emulate biological neural networks, yet challenges remain in simulating the behavioral dynamics and constructing the structural frameworks of neural synapses. This paper examines the neuromorphic dynamics and synchronization of fractional-order memristive systems, highlighting their potential as artificial synapses in neuromorphic computing. A 3-D fractional-order circuit was developed based on mathematical modeling of locally active memristors, revealing diverse neurodynamic behaviors, including action potentials, oscillations, and spike bursting, under varying fractional-order indices and parameters. The fractional-order boundaries for neuromorphic behaviors were discussed, and dynamic variations across different initial conditions were analyzed. A fractional-order finite-time synchronization controller was designed to achieve effective behavioral synchronization between independent memristive synapses. These findings offer valuable insights into the dynamic complexity of fractional-order systems, paving the way for their application in the design of neuromorphic systems and artificial neural networks.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"197 ","pages":"Article 116469"},"PeriodicalIF":5.3,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143877544","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we describe an algorithm for approximating functions of the form $f(x)=int _{a}^{b} x^{mu } sigma (mu ) , {text{d}} mu $ over $[0,1]$, where $sigma (mu )$ is some signed Radon measure, or, more generally, of the form $f(x) = {{langle sigma (mu ), x^mu rangle }}$, where $sigma (mu )$ is some distribution supported on $[a,b]$, with $0 <a < b< infty $. One example from this class of functions is $x^{c} (log{x})^{m}=(-1)^{m} {{langle delta ^{(m)}(mu -c), x^mu rangle }}$, where $aleq c leq b$ and $m geq 0$ is an integer. Given the desired accuracy $varepsilon $ and the values of $a$ and $b$, our method determines a priori a collection of noninteger powers $t_{1}$, $t_{2}$, …, $t_{N}$, so that the functions are approximated by series of the form $f(x)approx sum _{j=1}^{N} c_{j} x^{t_{j}}$, and a set of collocation points $x_{1}$, $x_{2}$, …, $x_{N}$, such that the expansion coefficients can be found by collocating the function at these points. We prove that our method has a small uniform approximation error, which is proportional to $varepsilon $ multiplied by some small constants, and that the number of singular powers and collocation points grows as $N=O(log{frac{1}{varepsilon }})$. We demonstrate the performance of our algorithm with several numerical experiments.
{"title":"On the approximation of singular functions by series of noninteger powers","authors":"Mohan Zhao, Kirill Serkh","doi":"10.1093/imanum/draf006","DOIUrl":"https://doi.org/10.1093/imanum/draf006","url":null,"abstract":"In this paper, we describe an algorithm for approximating functions of the form $f(x)=int _{a}^{b} x^{mu } sigma (mu ) , {text{d}} mu $ over $[0,1]$, where $sigma (mu )$ is some signed Radon measure, or, more generally, of the form $f(x) = {{langle sigma (mu ), x^mu rangle }}$, where $sigma (mu )$ is some distribution supported on $[a,b]$, with $0 &lt;a &lt; b&lt; infty $. One example from this class of functions is $x^{c} (log{x})^{m}=(-1)^{m} {{langle delta ^{(m)}(mu -c), x^mu rangle }}$, where $aleq c leq b$ and $m geq 0$ is an integer. Given the desired accuracy $varepsilon $ and the values of $a$ and $b$, our method determines a priori a collection of noninteger powers $t_{1}$, $t_{2}$, …, $t_{N}$, so that the functions are approximated by series of the form $f(x)approx sum _{j=1}^{N} c_{j} x^{t_{j}}$, and a set of collocation points $x_{1}$, $x_{2}$, …, $x_{N}$, such that the expansion coefficients can be found by collocating the function at these points. We prove that our method has a small uniform approximation error, which is proportional to $varepsilon $ multiplied by some small constants, and that the number of singular powers and collocation points grows as $N=O(log{frac{1}{varepsilon }})$. We demonstrate the performance of our algorithm with several numerical experiments.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"32 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143878121","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-04-25DOI: 10.1016/j.jde.2025.113356
Chunpeng Wang, Zihao Zhang
This paper concerns the existence and stability of smooth axisymmetric subsonic spiral flows with self-gravitation in a concentric cylinder. Firstly, the existence and uniqueness of smooth cylindrically symmetric subsonic spiral flows with self-gravitation are proved. Then we establish the structural stability of this background subsonic flows under axisymmetric perturbations of suitable boundary conditions, which yields the existence and uniqueness of smooth axisymmetric subsonic spiral flows with nonzero angular velocity and vorticity to the steady self-gravitating Euler-Poisson system. By the stream function formulation, the steady Euler-Poisson system for the axisymmetric self-gravitating flows can be decomposed into a second-order nonlinear elliptic system coupled with several transport equations. The key ingredient of the analysis is to discover a special structure of the associated elliptic system for the stream function and the gravitational potential, which enable us to obtain a priori estimates for the linearized elliptic problem.
{"title":"Structural stability of smooth axisymmetric subsonic spiral flows with self-gravitation in a concentric cylinder","authors":"Chunpeng Wang, Zihao Zhang","doi":"10.1016/j.jde.2025.113356","DOIUrl":"10.1016/j.jde.2025.113356","url":null,"abstract":"<div><div>This paper concerns the existence and stability of smooth axisymmetric subsonic spiral flows with self-gravitation in a concentric cylinder. Firstly, the existence and uniqueness of smooth cylindrically symmetric subsonic spiral flows with self-gravitation are proved. Then we establish the structural stability of this background subsonic flows under axisymmetric perturbations of suitable boundary conditions, which yields the existence and uniqueness of smooth axisymmetric subsonic spiral flows with nonzero angular velocity and vorticity to the steady self-gravitating Euler-Poisson system. By the stream function formulation, the steady Euler-Poisson system for the axisymmetric self-gravitating flows can be decomposed into a second-order nonlinear elliptic system coupled with several transport equations. The key ingredient of the analysis is to discover a special structure of the associated elliptic system for the stream function and the gravitational potential, which enable us to obtain a priori estimates for the linearized elliptic problem.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"438 ","pages":"Article 113356"},"PeriodicalIF":2.4,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143870201","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-04-25DOI: 10.1016/j.jde.2025.113359
Shu Wang, Shuzhen Zhang
We consider the initial value problem to the fractional generalized compressible Navier-Stokes-Poisson equations for viscous fluids with one Levy diffusion process in which the viscosity term appeared in the fluid equations and the diffusion term for the internal electrostatic potential are described respectively by the nonlocal fractional Laplace operators. The global-in-time existence of the smooth solution is proven under the assumption that the initial data are given in a small neighborhood of a constant state in the sense of Sobolev's space. The optimal decay rates depending upon the orders of two fractional Laplace operators are established, and that the momentum of the fractional Navier-Stokes-Poisson system exhibits a slower convergence rate in time to the constant state compared to that of the fractional compressible Navier-Stokes system is also shown.
{"title":"The initial value problem of the fractional compressible Navier-Stokes-Poisson system","authors":"Shu Wang, Shuzhen Zhang","doi":"10.1016/j.jde.2025.113359","DOIUrl":"10.1016/j.jde.2025.113359","url":null,"abstract":"<div><div>We consider the initial value problem to the fractional generalized compressible Navier-Stokes-Poisson equations for viscous fluids with one Levy diffusion process in which the viscosity term appeared in the fluid equations and the diffusion term for the internal electrostatic potential are described respectively by the nonlocal fractional Laplace operators. The global-in-time existence of the smooth solution is proven under the assumption that the initial data are given in a small neighborhood of a constant state in the sense of Sobolev's space. The optimal decay rates depending upon the orders of two fractional Laplace operators are established, and that the momentum of the fractional Navier-Stokes-Poisson system exhibits a slower convergence rate in time to the constant state compared to that of the fractional compressible Navier-Stokes system is also shown.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"438 ","pages":"Article 113359"},"PeriodicalIF":2.4,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143873891","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider a hybrid FEM-BEM method to compute approximations of full-space linear elliptic transmission problems. First, we derive a priori and a posteriori error estimates. Then, building on the latter, we present an adaptive algorithm and prove that it converges at optimal rates with respect to the number of mesh elements. Finally, we provide numerical experiments, demonstrating the practical performance of the adaptive algorithm.
{"title":"Optimal convergence rates of an adaptive hybrid FEM-BEM method for full-space linear transmission problems","authors":"Gregor Gantner, Michele Ruggeri","doi":"10.1093/imanum/draf023","DOIUrl":"https://doi.org/10.1093/imanum/draf023","url":null,"abstract":"We consider a hybrid FEM-BEM method to compute approximations of full-space linear elliptic transmission problems. First, we derive a priori and a posteriori error estimates. Then, building on the latter, we present an adaptive algorithm and prove that it converges at optimal rates with respect to the number of mesh elements. Finally, we provide numerical experiments, demonstrating the practical performance of the adaptive algorithm.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"13 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143875731","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-04-25DOI: 10.1016/j.jde.2025.113355
Yu Gao
This paper investigates a generalized hyperelastic-rod wave equation within its generalized framework. For conservative solutions, we establish that the singularities of the energy measure can only occur at countably many times. Furthermore, we prove the uniqueness of the solution by employing a refined characteristics method.
{"title":"On conservative solutions to the generalized hyperelastic-rod equation","authors":"Yu Gao","doi":"10.1016/j.jde.2025.113355","DOIUrl":"10.1016/j.jde.2025.113355","url":null,"abstract":"<div><div>This paper investigates a generalized hyperelastic-rod wave equation within its generalized framework. For conservative solutions, we establish that the singularities of the energy measure can only occur at countably many times. Furthermore, we prove the uniqueness of the solution by employing a refined characteristics method.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"438 ","pages":"Article 113355"},"PeriodicalIF":2.4,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143870197","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-04-25DOI: 10.1016/j.camwa.2025.04.005
Abu Naser Sarker , Ronald D. Haynes , Michael Robertson
An adaptive moving mesh or r-refinement method for the numerical approximation of pitting corrosion in heterogeneous materials is designed and applied to the problem of pitting corrosion in metals. The pitting corrosion is described by Laplace's equation with a moving boundary where the moving boundary problem is coupled with the partial differential equations describing the mesh movement. We show that the numerical approach is able to track evolving pit geometry for complicated materials with varying crystallography, corrosion-resistant inclusions, and material voids.
{"title":"A moving mesh method for pitting corrosion of heterogeneous materials","authors":"Abu Naser Sarker , Ronald D. Haynes , Michael Robertson","doi":"10.1016/j.camwa.2025.04.005","DOIUrl":"10.1016/j.camwa.2025.04.005","url":null,"abstract":"<div><div>An adaptive moving mesh or <em>r</em>-refinement method for the numerical approximation of pitting corrosion in heterogeneous materials is designed and applied to the problem of pitting corrosion in metals. The pitting corrosion is described by Laplace's equation with a moving boundary where the moving boundary problem is coupled with the partial differential equations describing the mesh movement. We show that the numerical approach is able to track evolving pit geometry for complicated materials with varying crystallography, corrosion-resistant inclusions, and material voids.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"191 ","pages":"Pages 48-59"},"PeriodicalIF":2.9,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143874705","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-04-25DOI: 10.1016/j.jde.2025.113349
Shangjiang Guo
In this paper, we consider a parabolic problem with a nonlinear boundary condition which is induced by the incoming flux on the boundary. We focus on analyzing the existence and stability of bifurcating positive solutions emanating from trivial solutions. Our approach combines the Lyapunov-Schmidt method with classical local bifurcation theory, extending the framework established by Crandall and Rabinowitz. The results provide new insights into the structure and stability properties of solutions under nonlinear flux boundary effects.
{"title":"Existence and stability of positive solutions in a parabolic problem with a nonlinear incoming flux on the boundary","authors":"Shangjiang Guo","doi":"10.1016/j.jde.2025.113349","DOIUrl":"10.1016/j.jde.2025.113349","url":null,"abstract":"<div><div>In this paper, we consider a parabolic problem with a nonlinear boundary condition which is induced by the incoming flux on the boundary. We focus on analyzing the existence and stability of bifurcating positive solutions emanating from trivial solutions. Our approach combines the Lyapunov-Schmidt method with classical local bifurcation theory, extending the framework established by Crandall and Rabinowitz. The results provide new insights into the structure and stability properties of solutions under nonlinear flux boundary effects.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"436 ","pages":"Article 113349"},"PeriodicalIF":2.4,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143868174","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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