Abstract As COVID-19 cases continue to rise globally, many researchers have developed mathematical models to help capture the dynamics of the spread of COVID-19. Specifically, the compartmental SEIR model and its variations have been widely employed. These models differ in the type of compartments included, nature of the transmission rates, seasonality, and several other factors. Yet, while the spread of COVID-19 is largely attributed to a wide range of social behaviors in the population, several of these SEIR models do not account for such behaviors. In this project, we consider novel SEIR-based models that incorporate various behaviors. We created a baseline model and explored incorporating both explicit and implicit behavioral changes. Furthermore, using the Next Generation Matrix method, we derive a basic reproduction number, which indicates the estimated number of secondary cases by a single infected individual. Numerical simulations for the various models we made were performed and user-friendly graphical user interfaces were created. In the future, we plan to expand our project to account for the use of face masks, age-based behaviors and transmission rates, and mixing patterns.
{"title":"Mathematical modeling, analysis, and simulation of the COVID-19 pandemic with explicit and implicit behavioral changes","authors":"Comfort Ohajunwa, Kirthi Kumar, P. Seshaiyer","doi":"10.1515/cmb-2020-0113","DOIUrl":"https://doi.org/10.1515/cmb-2020-0113","url":null,"abstract":"Abstract As COVID-19 cases continue to rise globally, many researchers have developed mathematical models to help capture the dynamics of the spread of COVID-19. Specifically, the compartmental SEIR model and its variations have been widely employed. These models differ in the type of compartments included, nature of the transmission rates, seasonality, and several other factors. Yet, while the spread of COVID-19 is largely attributed to a wide range of social behaviors in the population, several of these SEIR models do not account for such behaviors. In this project, we consider novel SEIR-based models that incorporate various behaviors. We created a baseline model and explored incorporating both explicit and implicit behavioral changes. Furthermore, using the Next Generation Matrix method, we derive a basic reproduction number, which indicates the estimated number of secondary cases by a single infected individual. Numerical simulations for the various models we made were performed and user-friendly graphical user interfaces were created. In the future, we plan to expand our project to account for the use of face masks, age-based behaviors and transmission rates, and mixing patterns.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"8 1","pages":"216 - 232"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/cmb-2020-0113","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42360705","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
F. Atici, Ngoc Nguyen, Kamala Dadashova, S. E. Pedersen, G. Koch
Abstract We study the h-discrete and h-discrete fractional representation of a pharmacokinetics-pharmacodynamics (PK-PD) model describing tumor growth and anticancer effects in continuous time considering a time scale h0, where h > 0. Since the measurements of the drug concentration in plasma were taken hourly, we consider h = 1/24 and obtain the model in discrete time (i.e. hourly). We then continue with fractionalizing the h-discrete nabla operator in the h-discrete model to obtain the model as a system of nabla h-fractional difference equations. In order to solve the fractional h-discrete system analytically we state and prove some theorems in the theory of discrete fractional calculus. After estimating and getting confidence intervals of the model parameters, we compare residual squared sum values of the models in one table. Our study shows that the new introduced models provide fitting as good as the existing models in continuous time.
{"title":"Pharmacokinetics and Pharmacodynamics Models of Tumor Growth and Anticancer Effects in Discrete Time","authors":"F. Atici, Ngoc Nguyen, Kamala Dadashova, S. E. Pedersen, G. Koch","doi":"10.1515/cmb-2020-0105","DOIUrl":"https://doi.org/10.1515/cmb-2020-0105","url":null,"abstract":"Abstract We study the h-discrete and h-discrete fractional representation of a pharmacokinetics-pharmacodynamics (PK-PD) model describing tumor growth and anticancer effects in continuous time considering a time scale h0, where h > 0. Since the measurements of the drug concentration in plasma were taken hourly, we consider h = 1/24 and obtain the model in discrete time (i.e. hourly). We then continue with fractionalizing the h-discrete nabla operator in the h-discrete model to obtain the model as a system of nabla h-fractional difference equations. In order to solve the fractional h-discrete system analytically we state and prove some theorems in the theory of discrete fractional calculus. After estimating and getting confidence intervals of the model parameters, we compare residual squared sum values of the models in one table. Our study shows that the new introduced models provide fitting as good as the existing models in continuous time.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"8 1","pages":"114 - 125"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/cmb-2020-0105","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42795192","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We wondered that if a reaction-diffusion model considering only the mean daily movement of susceptible, exposed and asymptomatic individuals was enough to describe the spread of the COVID-19 virus. The model was calibrated using data on the confirmed infection and death from France as well as their initial spatial distribution. First, the system of partial differential equations is studied, then the basic reproduction number, 0 is derived. Second, numerical simulations, based on a combination of level-set and finite differences, shown the spatial spread of COVID-19 from March 16 to June 16. Finally, scenarios of unlockdown are compared according to variation of distancing, or partially spatial lockdown.
{"title":"A reaction-diffusion system to better comprehend the unlockdown: Application of SEIR-type model with diffusion to the spatial spread of COVID-19 in France","authors":"Y. Mammeri","doi":"10.1515/cmb-2020-0104","DOIUrl":"https://doi.org/10.1515/cmb-2020-0104","url":null,"abstract":"Abstract We wondered that if a reaction-diffusion model considering only the mean daily movement of susceptible, exposed and asymptomatic individuals was enough to describe the spread of the COVID-19 virus. The model was calibrated using data on the confirmed infection and death from France as well as their initial spatial distribution. First, the system of partial differential equations is studied, then the basic reproduction number, 0 is derived. Second, numerical simulations, based on a combination of level-set and finite differences, shown the spatial spread of COVID-19 from March 16 to June 16. Finally, scenarios of unlockdown are compared according to variation of distancing, or partially spatial lockdown.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"8 1","pages":"102 - 113"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/cmb-2020-0104","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43182702","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-01DOI: 10.1101/2020.06.19.20135640
M. Grinfeld, P. Mulheran
Abstract We present an elementary model of COVID-19 propagation that makes explicit the connection between testing strategies and rates of transmission and the linear growth in new cases observed in many parts of the world.
{"title":"On Linear Growth in COVID-19 Cases","authors":"M. Grinfeld, P. Mulheran","doi":"10.1101/2020.06.19.20135640","DOIUrl":"https://doi.org/10.1101/2020.06.19.20135640","url":null,"abstract":"Abstract We present an elementary model of COVID-19 propagation that makes explicit the connection between testing strategies and rates of transmission and the linear growth in new cases observed in many parts of the world.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"8 1","pages":"211 - 215"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45583788","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The morphometric approach [11, 14] writes the solvation free energy as a linear combination of weighted versions of the volume, area, mean curvature, and Gaussian curvature of the space-filling diagram. We give a formula for the derivative of the weighted Gaussian curvature. Together with the derivatives of the weighted volume in [7], the weighted area in [4], and the weighted mean curvature in [1], this yields the derivative of the morphometric expression of solvation free energy.
{"title":"The Weighted Gaussian Curvature Derivative of a Space-Filling Diagram","authors":"A. Akopyan, H. Edelsbrunner","doi":"10.1515/cmb-2020-0101","DOIUrl":"https://doi.org/10.1515/cmb-2020-0101","url":null,"abstract":"Abstract The morphometric approach [11, 14] writes the solvation free energy as a linear combination of weighted versions of the volume, area, mean curvature, and Gaussian curvature of the space-filling diagram. We give a formula for the derivative of the weighted Gaussian curvature. Together with the derivatives of the weighted volume in [7], the weighted area in [4], and the weighted mean curvature in [1], this yields the derivative of the morphometric expression of solvation free energy.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"8 1","pages":"74 - 88"},"PeriodicalIF":0.0,"publicationDate":"2019-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/cmb-2020-0101","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46644764","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Representing an atom by a solid sphere in 3-dimensional Euclidean space, we get the space-filling diagram of a molecule by taking the union. Molecular dynamics simulates its motion subject to bonds and other forces, including the solvation free energy. The morphometric approach [12, 17] writes the latter as a linear combination of weighted versions of the volume, area, mean curvature, and Gaussian curvature of the space-filling diagram. We give a formula for the derivative of the weighted mean curvature. Together with the derivatives of the weighted volume in [7], the weighted area in [3], and the weighted Gaussian curvature [1], this yields the derivative of the morphometric expression of the solvation free energy.
{"title":"The Weighted Mean Curvature Derivative of a Space-Filling Diagram","authors":"A. Akopyan, H. Edelsbrunner","doi":"10.1515/cmb-2020-0100","DOIUrl":"https://doi.org/10.1515/cmb-2020-0100","url":null,"abstract":"Abstract Representing an atom by a solid sphere in 3-dimensional Euclidean space, we get the space-filling diagram of a molecule by taking the union. Molecular dynamics simulates its motion subject to bonds and other forces, including the solvation free energy. The morphometric approach [12, 17] writes the latter as a linear combination of weighted versions of the volume, area, mean curvature, and Gaussian curvature of the space-filling diagram. We give a formula for the derivative of the weighted mean curvature. Together with the derivatives of the weighted volume in [7], the weighted area in [3], and the weighted Gaussian curvature [1], this yields the derivative of the morphometric expression of the solvation free energy.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"8 1","pages":"51 - 67"},"PeriodicalIF":0.0,"publicationDate":"2019-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/cmb-2020-0100","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48942855","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We give a simple and practical algorithm to compute the link polynomials, which are defined according to the skein relations. Our method is based on a new total order on the set of all braid representatives. As by-product a new complete link invariant are obtained.
{"title":"A simple algorithm to compute link polynomials defined by using skein relations","authors":"Xuezhi Zhao","doi":"10.1515/cmb-2020-0102","DOIUrl":"https://doi.org/10.1515/cmb-2020-0102","url":null,"abstract":"Abstract We give a simple and practical algorithm to compute the link polynomials, which are defined according to the skein relations. Our method is based on a new total order on the set of all braid representatives. As by-product a new complete link invariant are obtained.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"8 1","pages":"68 - 73"},"PeriodicalIF":0.0,"publicationDate":"2019-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/cmb-2020-0102","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43454391","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The problem of determining which nucleotides of an RNA sequence are paired or unpaired in the secondary structure of an RNA, which we call RNA state inference, can be studied by different machine learning techniques. Successful state inference of RNA sequences can be used to generate auxiliary information for data-directed RNA secondary structure prediction. Typical tools for state inference, such as hidden Markov models, exhibit poor performance in RNA state inference, owing in part to their inability to recognize nonlocal dependencies. Bidirectional long short-term memory (LSTM) neural networks have emerged as a powerful tool that can model global nonlinear sequence dependencies and have achieved state-of-the-art performances on many different classification problems. This paper presents a practical approach to RNA secondary structure inference centered around a deep learning method for state inference. State predictions from a deep bidirectional LSTM are used to generate synthetic SHAPE data that can be incorporated into RNA secondary structure prediction via the Nearest Neighbor Thermodynamic Model (NNTM). This method produces predicted secondary structures for a diverse test set of 16S ribosomal RNA that are, on average, 25 percentage points more accurate than undirected MFE structures. Accuracy is highly dependent on the success of our state inference method, and investigating the global features of our state predictions reveals that accuracy of both our state inference and structure inference methods are highly dependent on the similarity of pairing patterns of the sequence to the training dataset. Availability of a large training dataset is critical to the success of this approach. Code available at https://github.com/dwillmott/rna-state-inf.
{"title":"Improving RNA secondary structure prediction via state inference with deep recurrent neural networks","authors":"Devin Willmott, D. Murrugarra, Q. Ye","doi":"10.1515/cmb-2020-0002","DOIUrl":"https://doi.org/10.1515/cmb-2020-0002","url":null,"abstract":"Abstract The problem of determining which nucleotides of an RNA sequence are paired or unpaired in the secondary structure of an RNA, which we call RNA state inference, can be studied by different machine learning techniques. Successful state inference of RNA sequences can be used to generate auxiliary information for data-directed RNA secondary structure prediction. Typical tools for state inference, such as hidden Markov models, exhibit poor performance in RNA state inference, owing in part to their inability to recognize nonlocal dependencies. Bidirectional long short-term memory (LSTM) neural networks have emerged as a powerful tool that can model global nonlinear sequence dependencies and have achieved state-of-the-art performances on many different classification problems. This paper presents a practical approach to RNA secondary structure inference centered around a deep learning method for state inference. State predictions from a deep bidirectional LSTM are used to generate synthetic SHAPE data that can be incorporated into RNA secondary structure prediction via the Nearest Neighbor Thermodynamic Model (NNTM). This method produces predicted secondary structures for a diverse test set of 16S ribosomal RNA that are, on average, 25 percentage points more accurate than undirected MFE structures. Accuracy is highly dependent on the success of our state inference method, and investigating the global features of our state predictions reveals that accuracy of both our state inference and structure inference methods are highly dependent on the similarity of pairing patterns of the sequence to the training dataset. Availability of a large training dataset is critical to the success of this approach. Code available at https://github.com/dwillmott/rna-state-inf.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"8 1","pages":"36 - 50"},"PeriodicalIF":0.0,"publicationDate":"2019-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/cmb-2020-0002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46581978","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The structural details of cellulose I β were discussed according to molecular dynamics simulations with the GLYCAM-06 force field. The simulation outcomes were in agreement with previous experimental data, including structural parameters and hydrogen bond pattern at 298 K. We found a new conformation of cellulose Iβ existed at the intermediate temperature that is between the low and high temperatures. Partial chain rotations along the backbone direction were found and conformations of hydroxymethyl groups that alternated from tg to either gt or gg were observed when the temperature increased from 298 K to 400 K. In addition, the gg conformation is preferred than gt. For the structure adopted at high temperature of 500 K, major chains were twisted and two chains detached from each plain. In contrast to the observation under intermediate temperature, the population of hydroxymethyl groups in gt exceeded that in gg conformation at high temperature. In addition, three patterns of hydrogen bonding were identified at low, intermediate and high temperatures in the simulations. The provided structural information indicated the transitions occurred around 350 K and 450 K, considered as the transitional temperatures of cellulose Iβ in this work.
{"title":"Thermal Response in Cellulose Iβ Based on Molecular Dynamics","authors":"Xuewei Jiang, Yu Chen, Yue Yuan, Lu Zheng","doi":"10.1515/cmb-2019-0007","DOIUrl":"https://doi.org/10.1515/cmb-2019-0007","url":null,"abstract":"Abstract The structural details of cellulose I β were discussed according to molecular dynamics simulations with the GLYCAM-06 force field. The simulation outcomes were in agreement with previous experimental data, including structural parameters and hydrogen bond pattern at 298 K. We found a new conformation of cellulose Iβ existed at the intermediate temperature that is between the low and high temperatures. Partial chain rotations along the backbone direction were found and conformations of hydroxymethyl groups that alternated from tg to either gt or gg were observed when the temperature increased from 298 K to 400 K. In addition, the gg conformation is preferred than gt. For the structure adopted at high temperature of 500 K, major chains were twisted and two chains detached from each plain. In contrast to the observation under intermediate temperature, the population of hydroxymethyl groups in gt exceeded that in gg conformation at high temperature. In addition, three patterns of hydrogen bonding were identified at low, intermediate and high temperatures in the simulations. The provided structural information indicated the transitions occurred around 350 K and 450 K, considered as the transitional temperatures of cellulose Iβ in this work.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"7 1","pages":"85 - 97"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/cmb-2019-0007","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47009650","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
G. S. Salas, A. E. L. Hernandez, Jiadi He, C. Karki, Yixin Xie, Shengjie Sun, Yuejiao Xian, Lin Li
Abstract Dengue viral capsid plays a significant role in viral life cycle of dengue, especially in vial genome protection and virus-cell fusion. Revealing mechanisms of the viral capsid protein assembly may lead to the discovery of anti-viral drugs that inhibit the assembly of the viral capsid. The E and M-proteins are arranged into heterotetramers, which consists of two copies of E and M-protein. The heterotetramers are assembled into a highly ordered capsid. While many investigations of the interactions between E and M-proteins have been performed, there are very few studies on the interactions between the heterotetramers and their roles in capsid assembly. Utilizing a series of computational approaches, this study focuses on the assembly mechanism of the heterotetramers. Our electrostatic analyses lead to the identification of four binding modes between each two dengue heterotetramers that repeat periodically throughout the virus capsid. Among these four binding modes, heterotetramers in binding modes I, II and IV are attractive. But in the binding mode III the heterotetramers repel each other, making mode III a suitable target for drug design. Furthermore, MD simulations were performed following by salt bridges analysis. This study demonstrates that using computational approaches is a promising direction to study the dengue virus.
{"title":"Using computational approaches to study dengue virus capsid assembly","authors":"G. S. Salas, A. E. L. Hernandez, Jiadi He, C. Karki, Yixin Xie, Shengjie Sun, Yuejiao Xian, Lin Li","doi":"10.1515/cmb-2019-0005","DOIUrl":"https://doi.org/10.1515/cmb-2019-0005","url":null,"abstract":"Abstract Dengue viral capsid plays a significant role in viral life cycle of dengue, especially in vial genome protection and virus-cell fusion. Revealing mechanisms of the viral capsid protein assembly may lead to the discovery of anti-viral drugs that inhibit the assembly of the viral capsid. The E and M-proteins are arranged into heterotetramers, which consists of two copies of E and M-protein. The heterotetramers are assembled into a highly ordered capsid. While many investigations of the interactions between E and M-proteins have been performed, there are very few studies on the interactions between the heterotetramers and their roles in capsid assembly. Utilizing a series of computational approaches, this study focuses on the assembly mechanism of the heterotetramers. Our electrostatic analyses lead to the identification of four binding modes between each two dengue heterotetramers that repeat periodically throughout the virus capsid. Among these four binding modes, heterotetramers in binding modes I, II and IV are attractive. But in the binding mode III the heterotetramers repel each other, making mode III a suitable target for drug design. Furthermore, MD simulations were performed following by salt bridges analysis. This study demonstrates that using computational approaches is a promising direction to study the dengue virus.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"7 1","pages":"64 - 72"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/cmb-2019-0005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42471344","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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