51
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Bos FM, Schreuder MJ, George SV, Doornbos B, Bruggeman R, van der Krieke L, Haarman BCM, Wichers M, Snippe E. Anticipating manic and depressive transitions in patients with bipolar disorder using early warning signals. Int J Bipolar Disord 2022; 10:12. [PMID: 35397076 PMCID: PMC8994809 DOI: 10.1186/s40345-022-00258-4] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 08/27/2021] [Accepted: 03/01/2022] [Indexed: 11/30/2022] Open
Abstract
Background In bipolar disorder treatment, accurate episode prediction is paramount but remains difficult. A novel idiographic approach to prediction is to monitor generic early warning signals (EWS), which may manifest in symptom dynamics. EWS could thus form personalized alerts in clinical care. The present study investigated whether EWS can anticipate manic and depressive transitions in individual patients with bipolar disorder. Methods Twenty bipolar type I/II patients (with ≥ 2 episodes in the previous year) participated in ecological momentary assessment (EMA), completing five questionnaires a day for four months (Mean = 491 observations per person). Transitions were determined by weekly completed questionnaires on depressive (Quick Inventory for Depressive Symptomatology Self-Report) and manic (Altman Self-Rating Mania Scale) symptoms. EWS (rises in autocorrelation at lag-1 and standard deviation) were calculated in moving windows over 17 affective and symptomatic EMA states. Positive and negative predictive values were calculated to determine clinical utility. Results Eleven patients reported 1–2 transitions. The presence of EWS increased the probability of impending depressive and manic transitions from 32-36% to 46–48% (autocorrelation) and 29–41% (standard deviation). However, the absence of EWS could not be taken as a sign that no transition would occur in the near future. The momentary states that indicated nearby transitions most accurately (predictive values: 65–100%) were full of ideas, worry, and agitation. Large individual differences in the utility of EWS were found. Conclusions EWS show theoretical promise in anticipating manic and depressive transitions in bipolar disorder, but the level of false positives and negatives, as well as the heterogeneity within and between individuals and preprocessing methods currently limit clinical utility. Supplementary Information The online version contains supplementary material available at 10.1186/s40345-022-00258-4.
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Affiliation(s)
- Fionneke M Bos
- Department of Psychiatry, Rob Giel Research Center, University of Groningen, University Medical Center Groningen, PO Box 30.001, 9700 RB, Groningen, The Netherlands. .,Department of Psychiatry, Interdisciplinary Center Psychopathology and Emotion Regulation (ICPE), University of Groningen, University Medical Center Groningen, Groningen, The Netherlands.
| | - Marieke J Schreuder
- Department of Psychiatry, Interdisciplinary Center Psychopathology and Emotion Regulation (ICPE), University of Groningen, University Medical Center Groningen, Groningen, The Netherlands
| | - Sandip V George
- Department of Psychiatry, Interdisciplinary Center Psychopathology and Emotion Regulation (ICPE), University of Groningen, University Medical Center Groningen, Groningen, The Netherlands.,Department of Computer Science , University College London , London, United Kingdom
| | - Bennard Doornbos
- Lentis Research, Lentis Psychiatric Institute, Groningen, The Netherlands
| | - Richard Bruggeman
- Department of Psychiatry, Rob Giel Research Center, University of Groningen, University Medical Center Groningen, PO Box 30.001, 9700 RB, Groningen, The Netherlands
| | - Lian van der Krieke
- Department of Psychiatry, Rob Giel Research Center, University of Groningen, University Medical Center Groningen, PO Box 30.001, 9700 RB, Groningen, The Netherlands.,Department of Psychiatry, Interdisciplinary Center Psychopathology and Emotion Regulation (ICPE), University of Groningen, University Medical Center Groningen, Groningen, The Netherlands
| | - Bartholomeus C M Haarman
- Department of Psychiatry, Interdisciplinary Center Psychopathology and Emotion Regulation (ICPE), University of Groningen, University Medical Center Groningen, Groningen, The Netherlands.,Department of Psychiatry, University Medical Center Groningen, University of Groningen, Groningen, The Netherlands
| | - Marieke Wichers
- Department of Psychiatry, Interdisciplinary Center Psychopathology and Emotion Regulation (ICPE), University of Groningen, University Medical Center Groningen, Groningen, The Netherlands
| | - Evelien Snippe
- Department of Psychiatry, Interdisciplinary Center Psychopathology and Emotion Regulation (ICPE), University of Groningen, University Medical Center Groningen, Groningen, The Netherlands
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van den Ende MW, Epskamp S, Lees MH, van der Maas HL, Wiers RW, Sloot PM. A review of mathematical modeling of addiction regarding both (neuro-) psychological processes and the social contagion perspectives. Addict Behav 2022; 127:107201. [PMID: 34959078 DOI: 10.1016/j.addbeh.2021.107201] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2020] [Revised: 07/04/2021] [Accepted: 11/22/2021] [Indexed: 12/16/2022]
Abstract
Addiction is a complex biopsychosocial phenomenon, impacted by biological predispositions, psychological processes, and the social environment. Using mathematical and computational models that allow for surrogative reasoning may be a promising avenue for gaining a deeper understanding of this complex behavior. This paper reviews and classifies a selection of formal models of addiction focusing on the intra- and inter-individual dynamics, i.e., (neuro) psychological models and social models. We find that these modeling approaches to addiction are too disjoint and argue that in order to unravel the complexities of biopsychosocial processes of addiction, models should integrate intra- and inter-individual factors.
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Hovmand PS, Calzada EJ, Gulbas LE, Kim SY, Chung S, Kuhlberg J, Hausmann-Stabile C, Zayas LH. System Dynamics of Cognitive Vulnerabilities and Family Support Among Latina Children and Adolescents. Clin Child Fam Psychol Rev 2022; 25:131-149. [PMID: 35244814 PMCID: PMC8948134 DOI: 10.1007/s10567-022-00395-3] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 02/14/2022] [Indexed: 11/28/2022]
Abstract
The paper describes an approach to developing a data-driven development of a feedback theory of cognitive vulnerabilities and family support focused on understanding the dynamics experienced among Latina children, adolescents, and families. Family support is understood to be a response to avoidant and maladaptive behaviors that may be characteristic of cognitive vulnerabilities commonly associated depression and suicidal ideation. A formal feedback theory is developed, appraised, and analyzed using a combination of secondary analysis of qualitative interviews (N = 30) and quantitative analysis using system dynamics modeling and simulation. Implications for prevention practice, treatment, and future research are discussed.
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Affiliation(s)
- Peter S Hovmand
- School of Medicine, Case Western Reserve University, Cleveland, USA.
| | - Esther J Calzada
- Steve Hicks School of Social Work, The University of Texas, Austin, USA
| | - Lauren E Gulbas
- Steve Hicks School of Social Work, The University of Texas, Austin, USA
| | - Su Yeon Kim
- Department of Human Ecology, The University of Texas, Austin, USA
| | | | | | | | - Luis H Zayas
- Steve Hicks School of Social Work, The University of Texas, Austin, USA
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54
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Robson DN, Li JM. A dynamical systems view of neuroethology: Uncovering stateful computation in natural behaviors. Curr Opin Neurobiol 2022; 73:102517. [PMID: 35217311 DOI: 10.1016/j.conb.2022.01.002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2021] [Revised: 01/06/2022] [Accepted: 01/11/2022] [Indexed: 11/03/2022]
Abstract
State-dependent computation is key to cognition in both biological and artificial systems. Alan Turing recognized the power of stateful computation when he created the Turing machine with theoretically infinite computational capacity in 1936. Independently, by 1950, ethologists such as Tinbergen and Lorenz also began to implicitly embed rudimentary forms of state-dependent computation to create qualitative models of internal drives and naturally occurring animal behaviors. Here, we reformulate core ethological concepts in explicitly dynamical systems terms for stateful computation. We examine, based on a wealth of recent neural data collected during complex innate behaviors across species, the neural dynamics that determine the temporal structure of internal states. We will also discuss the degree to which the brain can be hierarchically partitioned into nested dynamical systems and the need for a multi-dimensional state-space model of the neuromodulatory system that underlies motivational and affective states.
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Affiliation(s)
- Drew N Robson
- Max Planck Institute for Biological Cybernetics, Tuebingen, Germany.
| | - Jennifer M Li
- Max Planck Institute for Biological Cybernetics, Tuebingen, Germany.
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55
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Hametner C, Böhler L, Kozek M, Bartlechner J, Ecker O, Du ZP, Kölbl R, Bergmann M, Bachleitner-Hofmann T, Jakubek S. Intensive care unit occupancy predictions in the COVID-19 pandemic based on age-structured modelling and differential flatness. Nonlinear Dyn 2022; 109:57-75. [PMID: 35221526 PMCID: PMC8856937 DOI: 10.1007/s11071-022-07267-z] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/15/2021] [Accepted: 12/23/2021] [Indexed: 06/14/2023]
Abstract
The COVID-19 pandemic confronts governments and their health systems with great challenges for disease management. In many countries, hospitalization and in particular ICU occupancy is the primary measure for policy makers to decide on possible non-pharmaceutical interventions. In this paper a combined methodology for the prediction of COVID-19 case numbers, case-specific hospitalization and ICU admission rates as well as hospital and ICU occupancies is proposed. To this end, we employ differential flatness to provide estimates of the states of an epidemiological compartmental model and estimates of the unknown exogenous inputs driving its nonlinear dynamics. A main advantage of this method is that it requires the reported infection cases as the only data source. As vaccination rates and case-specific ICU rates are both strongly age-dependent, specifically an age-structured compartmental model is proposed to estimate and predict the spread of the epidemic across different age groups. By utilizing these predictions, case-specific hospitalization and case-specific ICU rates are subsequently estimated using deconvolution techniques. In an analysis of various countries we demonstrate how the methodology is able to produce real-time state estimates and hospital/ICU occupancy predictions for several weeks thus providing a sound basis for policy makers.
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Affiliation(s)
- Christoph Hametner
- Institute of Mechanics and Mechatronics, TU Wien, Getreidemarkt 9, 1060 Vienna, Austria
| | - Lukas Böhler
- Institute of Mechanics and Mechatronics, TU Wien, Getreidemarkt 9, 1060 Vienna, Austria
| | - Martin Kozek
- Institute of Mechanics and Mechatronics, TU Wien, Getreidemarkt 9, 1060 Vienna, Austria
| | - Johanna Bartlechner
- Institute of Mechanics and Mechatronics, TU Wien, Getreidemarkt 9, 1060 Vienna, Austria
| | - Oliver Ecker
- Institute of Mechanics and Mechatronics, TU Wien, Getreidemarkt 9, 1060 Vienna, Austria
| | - Zhang Peng Du
- Institute of Mechanics and Mechatronics, TU Wien, Getreidemarkt 9, 1060 Vienna, Austria
| | - Robert Kölbl
- Institute of Mechanics and Mechatronics, TU Wien, Getreidemarkt 9, 1060 Vienna, Austria
| | - Michael Bergmann
- Division of Visceral Surgery, Department of General Surgery, Medical University of Vienna, Vienna, Austria
- Comprehensive Cancer Center, Medical University of Vienna, Vienna, Austria
| | - Thomas Bachleitner-Hofmann
- Division of Visceral Surgery, Department of General Surgery, Medical University of Vienna, Vienna, Austria
- Comprehensive Cancer Center, Medical University of Vienna, Vienna, Austria
| | - Stefan Jakubek
- Institute of Mechanics and Mechatronics, TU Wien, Getreidemarkt 9, 1060 Vienna, Austria
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56
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Garfinkel A, Bennoun S, Deeds E, Van Valkenburgh B. Teaching Dynamics to Biology Undergraduates: the UCLA Experience. Bull Math Biol 2022; 84:43. [PMID: 35150346 PMCID: PMC8840928 DOI: 10.1007/s11538-022-00999-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2021] [Accepted: 01/18/2022] [Indexed: 11/27/2022]
Abstract
There is a growing realization that traditional “Calculus for Life Sciences” courses do not show their applicability to the Life Sciences and discourage student interest. There have been calls from the AAAS, the Howard Hughes Medical Institute, the NSF, and the American Association of Medical Colleges for a new kind of math course for biology students, that would focus on dynamics and modeling, to understand positive and negative feedback relations, in the context of important biological applications, not incidental “examples.” We designed a new course, LS 30, based on the idea of modeling biological relations as dynamical systems, and then visualizing the dynamical system as a vector field, assigning “change vectors” to every point in a state space. The resulting course, now being given to approximately 1400 students/year at UCLA, has greatly improved student perceptions toward math in biology, reduced minority performance gaps, and increased students' subsequent grades in physics and chemistry courses. This new course can be customized easily for a broad range of institutions. All course materials, including lecture plans, labs, homeworks and exams, are available from the authors; supporting videos are posted online.
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Affiliation(s)
- Alan Garfinkel
- Integrative Biology and Physiology, University of California, Los Angeles, CA, 90095, USA.
| | - Steve Bennoun
- Psychology Department, University of California, Los Angeles, CA, 90095, USA
| | - Eric Deeds
- Integrative Biology and Physiology, University of California, Los Angeles, CA, 90095, USA
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Browne CJ, Gulbudak H, Macdonald JC. Differential impacts of contact tracing and lockdowns on outbreak size in COVID-19 model applied to China. J Theor Biol 2022; 532:110919. [PMID: 34592263 DOI: 10.1016/j.jtbi.2021.110919] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2020] [Revised: 09/20/2021] [Accepted: 09/22/2021] [Indexed: 02/07/2023]
Abstract
The COVID-19 pandemic has led to widespread attention given to the notions of “flattening the curve” during lockdowns, and successful contact tracing programs suppressing outbreaks. However a more nuanced picture of these interventions’ effects on epidemic trajectories is necessary. By mathematical modeling each as reactive quarantine measures, dependent on current infection rates, with different mechanisms of action, we analytically derive distinct nonlinear effects of these interventions on final and peak outbreak size. We simultaneously fit the model to provincial reported case and aggregated quarantined contact data from China. Lockdowns compressed the outbreak in China inversely proportional to population quarantine rates, revealing their critical dependence on timing. Contact tracing had significantly less impact on final outbreak size, but did lead to peak size reduction. Our analysis suggests that altering the cumulative cases in a rapidly spreading outbreak requires sustained interventions that decrease the reproduction number close to one, otherwise some type of swift lockdown measure may be needed.
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58
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Benkő Z, Stippinger M, Rehus R, Bencze A, Fabó D, Hajnal B, Eröss LG, Telcs A, Somogyvári Z. Manifold-adaptive dimension estimation revisited. PeerJ Comput Sci 2022; 8:e790. [PMID: 35111907 PMCID: PMC8771813 DOI: 10.7717/peerj-cs.790] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/08/2021] [Accepted: 11/01/2021] [Indexed: 06/14/2023]
Abstract
Data dimensionality informs us about data complexity and sets limit on the structure of successful signal processing pipelines. In this work we revisit and improve the manifold adaptive Farahmand-Szepesvári-Audibert (FSA) dimension estimator, making it one of the best nearest neighbor-based dimension estimators available. We compute the probability density function of local FSA estimates, if the local manifold density is uniform. Based on the probability density function, we propose to use the median of local estimates as a basic global measure of intrinsic dimensionality, and we demonstrate the advantages of this asymptotically unbiased estimator over the previously proposed statistics: the mode and the mean. Additionally, from the probability density function, we derive the maximum likelihood formula for global intrinsic dimensionality, if i.i.d. holds. We tackle edge and finite-sample effects with an exponential correction formula, calibrated on hypercube datasets. We compare the performance of the corrected median-FSA estimator with kNN estimators: maximum likelihood (Levina-Bickel), the 2NN and two implementations of DANCo (R and MATLAB). We show that corrected median-FSA estimator beats the maximum likelihood estimator and it is on equal footing with DANCo for standard synthetic benchmarks according to mean percentage error and error rate metrics. With the median-FSA algorithm, we reveal diverse changes in the neural dynamics while resting state and during epileptic seizures. We identify brain areas with lower-dimensional dynamics that are possible causal sources and candidates for being seizure onset zones.
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Affiliation(s)
- Zsigmond Benkő
- Department of Computational Sciences, Wigner Research Centre for Physics, Budapest, Hungary
- János Szentágothai Doctoral School of Neurosciences, Semmelweis University, Budapest, Hungary
| | - Marcell Stippinger
- Department of Computational Sciences, Wigner Research Centre for Physics, Budapest, Hungary
| | - Roberta Rehus
- Department of Computational Sciences, Wigner Research Centre for Physics, Budapest, Hungary
| | - Attila Bencze
- Department of Computational Sciences, Wigner Research Centre for Physics, Budapest, Hungary
| | - Dániel Fabó
- Epilepsy Center, Department of Neurology, National Institute of Clinical Neurosciences, Budapest, Hungary
| | - Boglárka Hajnal
- János Szentágothai Doctoral School of Neurosciences, Semmelweis University, Budapest, Hungary
- Epilepsy Center, Department of Neurology, National Institute of Clinical Neurosciences, Budapest, Hungary
| | - Loránd G. Eröss
- Department of Functional Neurosurgery, National Institute of Clinical Neurosciences, Budapest, Hungary
- Faculty of Information Technology and Bionics, Péter Pázmány Catholic University, Budapest, Hungary
| | - András Telcs
- Department of Computational Sciences, Wigner Research Centre for Physics, Budapest, Hungary
- Department of Computer Science and Information Theory, Faculty of Electrical Engineering and Informatics, Budapest University of Technology and Economics, Budapest, Hungary
- Department of Quantitative Methods, Faculty of Business and Economics,, University of Pannonia, Veszprém, Hungary
| | - Zoltán Somogyvári
- Department of Computational Sciences, Wigner Research Centre for Physics, Budapest, Hungary
- Neuromicrosystems ltd., Budapest, Hungary
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Dávila-Velderrain J, Caldú-Primo JL, Martínez-García JC, Álvarez-Buylla Roces ME. Gene Regulatory Network Dynamical Logical Models for Plant Development. Methods Mol Biol 2022; 2395:59-77. [PMID: 34822149 DOI: 10.1007/978-1-0716-1816-5_4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Mathematical and computational approaches that integrate and model the concerted action of multiple genetic and nongenetic components holding highly nonlinear interactions are fundamental for the study of developmental processes. Among these, gene regulatory network (GRN) dynamical models are very useful to understand how diverse types of regulatory constraints restrict the multigene expression patterns that characterize different cell fates. In this chapter we present a hands-on approach to model GRN dynamics, taking as a working example a well-curated and experimentally grounded GRN developmental module proposed by our group: the flower organ specification gene regulatory network (FOS-GRN). We demonstrate how to build and analyze a GRN model according to the following steps: (1) integration of molecular genetic data and formulation of logical rules specifying the dynamic behavior of each gene; (2) determination of steady states (attractors) corresponding to each cell type; (3) validation of the GRN model; and (4) extension of the deterministic model with the inclusion of stochasticity in order to model cell-state transitions dependent on noise due to fluctuations of the involved gen products. The methodologies explained here in detail can be applied to any other developmental module.
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Affiliation(s)
- José Dávila-Velderrain
- Computer Science and Artificial Intelligence Lab, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - José Luis Caldú-Primo
- Laboratorio de Genética Molecular, Epigenética, Desarrollo y Evolución de Plantas, Instituto de Ecología, Universidad Nacional Autónoma de México, Ciudad Universitaria, CDMX, Coyoacán, México
- Centro de Ciencias de la Complejidad (C3), Universidad Nacional Autónoma de México, Ciudad Universitaria, CDMX, México
| | | | - María Elena Álvarez-Buylla Roces
- Laboratorio de Genética Molecular, Epigenética, Desarrollo y Evolución de Plantas, Instituto de Ecología, Universidad Nacional Autónoma de México, Ciudad Universitaria, CDMX, Coyoacán, México.
- Centro de Ciencias de la Complejidad (C3), Universidad Nacional Autónoma de México, Ciudad Universitaria, CDMX, México.
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60
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Fai TG, Park Y. Global asymptotic stability of the active disassembly model of flagellar length control. J Math Biol 2021; 84:8. [PMID: 34970717 DOI: 10.1007/s00285-021-01709-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2020] [Revised: 09/10/2021] [Accepted: 12/10/2021] [Indexed: 01/01/2023]
Abstract
Organelle size control is a fundamental question in biology that demonstrates the fascinating ability of cells to maintain homeostasis within their highly variable environments. Theoretical models describing cellular dynamics have the potential to help elucidate the principles underlying size control. Here, we perform a detailed study of the active disassembly model proposed in Fai et al. (elife 8:e42599, 2019). We construct a hybrid system which is shown to be well-behaved throughout the domain. We rule out the possibility of oscillations arising in the model and prove global asymptotic stability in the case of two flagella by the construction of a suitable Lyapunov function. Finally, we generalize the model to the case of arbitrary flagellar number in order to study olfactory sensory neurons, which have up to twenty cilia per cell. We show that our theoretical results may be extended to this case and explore the implications of this universal mechanism of size control.
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61
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Zhu A, Jin P, Tang Y. Approximation capabilities of measure-preserving neural networks. Neural Netw 2021; 147:72-80. [PMID: 34995951 DOI: 10.1016/j.neunet.2021.12.007] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2021] [Revised: 11/21/2021] [Accepted: 12/14/2021] [Indexed: 11/26/2022]
Abstract
Measure-preserving neural networks are well-developed invertible models, however, their approximation capabilities remain unexplored. This paper rigorously analyzes the approximation capabilities of existing measure-preserving neural networks including NICE and RevNets. It is shown that for compact U⊂RD with D≥2, the measure-preserving neural networks are able to approximate arbitrary measure-preserving map ψ:U→RD which is bounded and injective in the Lp-norm. In particular, any continuously differentiable injective map with ±1 determinant of Jacobian is measure-preserving, thus can be approximated.
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Affiliation(s)
- Aiqing Zhu
- LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China; School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Pengzhan Jin
- LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China; School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Yifa Tang
- LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China; School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China.
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62
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Han J, Perera S, Wunderlich Z, Periwal V. Mechanistic gene networks inferred from single-cell data with an outlier-insensitive method. Math Biosci 2021; 342:108722. [PMID: 34688607 PMCID: PMC8722367 DOI: 10.1016/j.mbs.2021.108722] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/20/2021] [Revised: 08/25/2021] [Accepted: 08/25/2021] [Indexed: 11/28/2022]
Abstract
With advances in single-cell techniques, measuring gene dynamics at cellular resolution has become practicable. In contrast, the increased complexity of data has made it more challenging computationally to unravel underlying biological mechanisms. Thus, it is critical to develop novel computational methods capable of dealing with such complexity and of providing predictive deductions from such data. Many methods have been developed to address such challenges, each with its own advantages and limitations. We present an iterative regression algorithm for inferring a mechanistic gene network from single-cell data, especially suited to overcoming problems posed by measurement outliers. Using this regression, we infer a developmental model for the gene dynamics in Drosophila melanogaster blastoderm embryo. Our results show that the predictive power of the inferred model is higher than that of other models inferred with least squares and ridge regressions. As a baseline for how well a mechanistic model should be expected to perform, we find that model predictions of the gene dynamics are more accurate than predictions made with neural networks of varying architectures and complexity. This holds true even in the limit of small sample sizes. We compare predictions for various gene knockouts with published experimental results, finding substantial qualitative agreement. We also make predictions for gene dynamics under various gene network perturbations, impossible in non-mechanistic models.
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Affiliation(s)
- Jungmin Han
- Laboratory of Biological Modeling, National Institutes of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, MD 20814, United States of America.
| | - Sudheesha Perera
- Laboratory of Biological Modeling, National Institutes of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, MD 20814, United States of America.
| | - Zeba Wunderlich
- Department of Developmental and Cell Biology, University of California, Irvine, CA 92617, United States of America.
| | - Vipul Periwal
- Laboratory of Biological Modeling, National Institutes of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, MD 20814, United States of America.
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63
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Koopmans L, Youk H. Predictive landscapes hidden beneath biological cellular automata. J Biol Phys 2021; 47:355-369. [PMID: 34739687 PMCID: PMC8603977 DOI: 10.1007/s10867-021-09592-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/04/2021] [Accepted: 10/14/2021] [Indexed: 11/11/2022] Open
Abstract
To celebrate Hans Frauenfelder's achievements, we examine energy(-like) "landscapes" for complex living systems. Energy landscapes summarize all possible dynamics of some physical systems. Energy(-like) landscapes can explain some biomolecular processes, including gene expression and, as Frauenfelder showed, protein folding. But energy-like landscapes and existing frameworks like statistical mechanics seem impractical for describing many living systems. Difficulties stem from living systems being high dimensional, nonlinear, and governed by many, tightly coupled constituents that are noisy. The predominant modeling approach is devising differential equations that are tailored to each living system. This ad hoc approach faces the notorious "parameter problem": models have numerous nonlinear, mathematical functions with unknown parameter values, even for describing just a few intracellular processes. One cannot measure many intracellular parameters or can only measure them as snapshots in time. Another modeling approach uses cellular automata to represent living systems as discrete dynamical systems with binary variables. Quantitative (Hamiltonian-based) rules can dictate cellular automata (e.g., Cellular Potts Model). But numerous biological features, in current practice, are qualitatively described rather than quantitatively (e.g., gene is (highly) expressed or not (highly) expressed). Cellular automata governed by verbal rules are useful representations for living systems and can mitigate the parameter problem. However, they can yield complex dynamics that are difficult to understand because the automata-governing rules are not quantitative and much of the existing mathematical tools and theorems apply to continuous but not discrete dynamical systems. Recent studies found ways to overcome this challenge. These studies either discovered or suggest an existence of predictive "landscapes" whose shapes are described by Lyapunov functions and yield "equations of motion" for a "pseudo-particle." The pseudo-particle represents the entire cellular lattice and moves on the landscape, thereby giving a low-dimensional representation of the cellular automata dynamics. We outline this promising modeling strategy.
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Affiliation(s)
- Lars Koopmans
- Program in Applied Physics, Delft University of Technology, Delft, The Netherlands
- Department of Systems Biology, University of Massachusetts Chan Medical School, Worcester, MA, USA
| | - Hyun Youk
- Department of Systems Biology, University of Massachusetts Chan Medical School, Worcester, MA, USA.
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64
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Fioriti V, Chinnici M, Arbore A, Sigismondi N, Roselli I. Estimating the epidemic growth dynamics within the first week. Heliyon 2021; 7:e08422. [PMID: 34816052 PMCID: PMC8600919 DOI: 10.1016/j.heliyon.2021.e08422] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2021] [Revised: 10/22/2021] [Accepted: 11/15/2021] [Indexed: 11/20/2022] Open
Abstract
Information about the early growth of infectious outbreaks is indispensable to estimate the epidemic spreading. A large number of mathematical tools have been developed to this end, facing as much large number of different dynamic evolutions, ranging from sub-linear to super-exponential growth. Of course, the crucial point is that we do not have enough data during the initial outbreak phase to make reliable inferences. Here we propose a straightforward methodology to estimate the epidemic growth dynamic from the cumulative infected data of just a week, provided a surveillance system is available over the whole territory. The methodology, based on the Newcomb-Benford Law, is applied to the Italian covid 19 case-study. Results show that it is possible to discriminate the epidemic dynamics using the first seven data points collected in fifty Italian cities. Moreover, the most probable approximating function of the growth within a six-week epidemic scenario is identified.
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Affiliation(s)
| | - Marta Chinnici
- ENEA- C.R Casaccia, Via Anguillarese 301, Rome, 00123, Italy
| | | | | | - Ivan Roselli
- ENEA- C.R Casaccia, Via Anguillarese 301, Rome, 00123, Italy
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65
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Guilberteau J, Pouchol C, Pouradier Duteil N. Monostability and bistability of biological switches. J Math Biol 2021; 83:65. [PMID: 34800197 DOI: 10.1007/s00285-021-01687-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2021] [Revised: 09/10/2021] [Accepted: 10/21/2021] [Indexed: 12/01/2022]
Abstract
Cell-fate transition can be modeled by ordinary differential equations (ODEs) which describe the behavior of several molecules in interaction, and for which each stable equilibrium corresponds to a possible phenotype (or 'biological trait'). In this paper, we focus on simple ODE systems modeling two molecules which each negatively (or positively) regulate the other. It is well-known that such models may lead to monostability or multistability, depending on the selected parameters. However, extensive numerical simulations have led systems biologists to conjecture that in the vast majority of cases, there cannot be more than two stable points. Our main result is a proof of this conjecture. More specifically, we provide a criterion ensuring at most bistability, which is indeed satisfied by most commonly used functions. This includes Hill functions, but also a wide family of convex and sigmoid functions. We also determine which parameters lead to monostability, and which lead to bistability, by developing a more general framework encompassing all our results.
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Affiliation(s)
- Jules Guilberteau
- Laboratoire Jacques-Louis Lions (LJLL), CNRS, Inria, Sorbonne Université and Université de Paris, 75005, Paris, France.
| | - Camille Pouchol
- FP2M, CNRS FR 2036, MAP5 UMR 8145, Université de Paris, 75006, Paris, France
| | - Nastassia Pouradier Duteil
- Laboratoire Jacques-Louis Lions (LJLL), CNRS, Inria, Sorbonne Université and Université de Paris, 75005, Paris, France
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66
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Berg M, Plöntzke J, Siebert H, Röblitz S. Modelling Oscillatory Patterns in the Bovine Estrous Cycle with Boolean Delay Equations. Bull Math Biol 2021; 83:121. [PMID: 34727249 PMCID: PMC8563642 DOI: 10.1007/s11538-021-00942-z] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2020] [Accepted: 09/08/2021] [Indexed: 11/25/2022]
Abstract
Boolean delay equations (BDEs), with their relatively simple and intuitive mode of modelling, have been used in many research areas including, for example, climate dynamics and earthquake propagation. Their application to biological systems has been scarce and limited to the molecular level. Here, we derive and present two BDE models. One is directly derived from a previously published ordinary differential equation (ODE) model for the bovine estrous cycle, whereas the second model includes a modification of a particular biological mechanism. We not only compare the simulation results from the BDE models with the trajectories of the ODE model, but also validate the BDE models with two additional numerical experiments. One experiment induces a switch in the oscillatory pattern upon changes in the model parameters, and the other simulates the administration of a hormone that is known to shift the estrous cycle in time. The models presented here are the first BDE models for hormonal oscillators, and the first BDE models for drug administration. Even though automatic parameter estimation still remains challenging, our results support the role of BDEs as a framework for the systematic modelling of complex biological oscillators.
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Affiliation(s)
| | | | - Heike Siebert
- Department of Mathematics and Computer Science, Freie Universität, Berlin, Germany
| | - Susanna Röblitz
- Computational Biology Unit, Department of Informatics, University of Bergen, Bergen, Norway
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67
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Surendran A, Forbes Dewey C, Low BC, Tucker-Kellogg L. A computational model of mutual antagonism in the mechano-signaling network of RhoA and nitric oxide. BMC Mol Cell Biol 2021; 22:47. [PMID: 34635055 PMCID: PMC8507106 DOI: 10.1186/s12860-021-00383-5] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/15/2021] [Accepted: 08/23/2021] [Indexed: 12/12/2022] Open
Abstract
BACKGROUND RhoA is a master regulator of cytoskeletal contractility, while nitric oxide (NO) is a master regulator of relaxation, e.g., vasodilation. There are multiple forms of cross-talk between the RhoA/ROCK pathway and the eNOS/NO/cGMP pathway, but previous work has not studied their interplay at a systems level. Literature review suggests that the majority of their cross-talk interactions are antagonistic, which motivates us to ask whether the RhoA and NO pathways exhibit mutual antagonism in vitro, and if so, to seek the theoretical implications of their mutual antagonism. RESULTS Experiments found mutual antagonism between RhoA and NO in epithelial cells. Since mutual antagonism is a common motif for bistability, we sought to explore through theoretical simulations whether the RhoA-NO network is capable of bistability. Qualitative modeling showed that there are parameters that can cause bistable switching in the RhoA-NO network, and that the robustness of the bistability would be increased by positive feedback between RhoA and mechanical tension. CONCLUSIONS We conclude that the RhoA-NO bistability is robust enough in silico to warrant the investment of further experimental testing. Tension-dependent bistability has the potential to create sharp concentration gradients, which could contribute to the localization and self-organization of signaling domains during cytoskeletal remodeling and cell migration.
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Affiliation(s)
- Akila Surendran
- Singapore-MIT Alliance, Computational Systems Biology Programme, National University of Singapore, Singapore, Singapore.,Centre for Assistive Technology & Innovation, National Institute of Speech & Hearing, Trivandrum, Kerala, India
| | - C Forbes Dewey
- Singapore-MIT Alliance, Computational Systems Biology Programme, National University of Singapore, Singapore, Singapore.,Biological Engineering and Mechanical Engineering Departments, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Boon Chuan Low
- Singapore-MIT Alliance, Computational Systems Biology Programme, National University of Singapore, Singapore, Singapore.,Department of Biological Sciences, National University of Singapore, Singapore, Singapore.,Mechanobiology Institute, National University of Singapore, Singapore, Singapore.,University Scholars Programme, National University of Singapore, Singapore, Singapore
| | - Lisa Tucker-Kellogg
- Singapore-MIT Alliance, Computational Systems Biology Programme, National University of Singapore, Singapore, Singapore. .,Cancer and Stem Cell Biology, and Centre for Computational Biology, Duke-NUS Medical School, Singapore, Singapore.
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68
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Wang W, Qu F, Li S, Wang L. Effects of motor skill level and speed on movement variability during running. J Biomech 2021; 127:110680. [PMID: 34418864 DOI: 10.1016/j.jbiomech.2021.110680] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/04/2021] [Revised: 07/23/2021] [Accepted: 08/01/2021] [Indexed: 11/20/2022]
Abstract
Variability in movement is an informative biological feature. This study aimed to examine the effects of motor skill level and running speed on movement variability. Twenty-nine male college students (fourteen athletes and fifteen non-athletes) participated in this study. All participants performed three motor tasks: 3 m/s running, 5 m/s running, and sprint running. Lower-limb kinematic data were acquired using a 16-camera infrared motion capture system. Lower-limb coordination during the stance phase was quantified using a continuous relative phase (CRP) method for interlimb (hip-hip, knee-knee, ankle-ankle) and intralimb (hip-knee, knee-ankle). The variabilities of stride length, stride cadence, joint angles, intralimb CRP, and interlimb CRP were calculated as standard deviations of each measurement. The results revealed that there were significant interaction effects between motor skill level and speed on movement variability for stride length (p = 0.047), ankle angle during propulsive phase (p = 0.001), knee-ankle CRP during propulsive phase (p = 0.007) and knee-knee CRP during propulsive phase (p = 0.009). Athletes showed greater angle variability, coordination variability and lower stride length variability during sprinting (all p < 0.05). In contrast, no between groups variability difference was observed when jogging at fixed lower speeds (all p > 0.05). Movement variability was greater for sprinting compared to jogging. Skill level was found to differentially affect the role of coordination variability in sprint performance. For athletes, hip-knee deviation phase and hip-hip deviation phase during braking phase were negatively correlated with sprinting speed (r = -0.563 and -0.642, respectively; both p < 0.05). For non-athletes, hip-knee deviation phase was positively correlated with sprinting speed (r = 0.581, p = 0.023). In conclusion, stride length become more stable, joint angle and coordination become more variable with long-term training. Results of this study also suggest that the relationship between coordination variability and performance is complicated and may depend on motor skill level. More longitudinal studies are needed to definitively determine the relationship between movement variability and performance.
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69
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Saha P, Dash S, Mukhopadhyay S. Physics-incorporated convolutional recurrent neural networks for source identification and forecasting of dynamical systems. Neural Netw 2021; 144:359-71. [PMID: 34547672 DOI: 10.1016/j.neunet.2021.08.033] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/23/2020] [Revised: 08/25/2021] [Accepted: 08/30/2021] [Indexed: 11/20/2022]
Abstract
Spatio-temporal dynamics of physical processes are generally modeled using partial differential equations (PDEs). Though the core dynamics follows some principles of physics, real-world physical processes are often driven by unknown external sources. In such cases, developing a purely analytical model becomes very difficult and data-driven modeling can be of assistance. In this paper, we present a hybrid framework combining physics-based numerical models with deep learning for source identification and forecasting of spatio-temporal dynamical systems with unobservable time-varying external sources. We formulate our model PhICNet as a convolutional recurrent neural network (RNN) which is end-to-end trainable for spatio-temporal evolution prediction of dynamical systems and learns the source behavior as an internal state of the RNN. Experimental results show that the proposed model can forecast the dynamics for a relatively long time and identify the sources as well.
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70
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Hametner C, Kozek M, Böhler L, Wasserburger A, Du ZP, Kölbl R, Bergmann M, Bachleitner-Hofmann T, Jakubek S. Estimation of exogenous drivers to predict COVID-19 pandemic using a method from nonlinear control theory. Nonlinear Dyn 2021; 106:1111-1125. [PMID: 34511723 PMCID: PMC8419820 DOI: 10.1007/s11071-021-06811-7] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/12/2021] [Accepted: 08/09/2021] [Indexed: 06/01/2023]
Abstract
The currently ongoing COVID-19 pandemic confronts governments and their health systems with great challenges for disease management. Epidemiological models play a crucial role, thereby assisting policymakers to predict the future course of infections and hospitalizations. One difficulty with current models is the existence of exogenous and unmeasurable variables and their significant effect on the infection dynamics. In this paper, we show how a method from nonlinear control theory can complement common compartmental epidemiological models. As a result, one can estimate and predict these exogenous variables requiring the reported infection cases as the only data source. The method allows to investigate how the estimates of exogenous variables are influenced by non-pharmaceutical interventions and how imminent epidemic waves could already be predicted at an early stage. In this way, the concept can serve as an "epidemometer" and guide the optimal timing of interventions. Analyses of the COVID-19 epidemic in various countries demonstrate the feasibility and potential of the proposed approach. The generic character of the method allows for straightforward extension to different epidemiological models.
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Affiliation(s)
- Christoph Hametner
- Institute of Mechanics and Mechatronics, TU Wien, Getreidemarkt 9, 1060 Vienna, Austria
| | - Martin Kozek
- Institute of Mechanics and Mechatronics, TU Wien, Getreidemarkt 9, 1060 Vienna, Austria
| | - Lukas Böhler
- Institute of Mechanics and Mechatronics, TU Wien, Getreidemarkt 9, 1060 Vienna, Austria
| | | | - Zhang Peng Du
- Institute of Mechanics and Mechatronics, TU Wien, Getreidemarkt 9, 1060 Vienna, Austria
| | - Robert Kölbl
- Institute of Mechanics and Mechatronics, TU Wien, Getreidemarkt 9, 1060 Vienna, Austria
| | - Michael Bergmann
- Division of Visceral Surgery, Department of General Surgery, Medical University of Vienna, Vienna, Austria
- Comprehensive Cancer Center, Medical University of Vienna, Vienna, Austria
| | - Thomas Bachleitner-Hofmann
- Division of Visceral Surgery, Department of General Surgery, Medical University of Vienna, Vienna, Austria
- Comprehensive Cancer Center, Medical University of Vienna, Vienna, Austria
| | - Stefan Jakubek
- Institute of Mechanics and Mechatronics, TU Wien, Getreidemarkt 9, 1060 Vienna, Austria
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71
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Abramov O, Bebell KL, Mojzsis SJ. Emergent Bioanalogous Properties of Blockchain-based Distributed Systems. ORIGINS LIFE EVOL B 2021; 51:131-165. [PMID: 34363563 DOI: 10.1007/s11084-021-09608-1] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2020] [Accepted: 03/27/2021] [Indexed: 11/24/2022]
Abstract
We apply a novel definition of biological systems to a series of reproducible observations on a blockchain-based distributed virtual machine (dVM). We find that such blockchain-based systems display a number of bioanalogous properties, such as response to the environment, growth and change, replication, and homeostasis, that fit some definitions of life. We further present a conceptual model for a simple self-sustaining, self-organizing, self-regulating distributed 'organism' as an operationally closed system that would fulfill all basic definitions and criteria for life, and describe developing technologies, particularly artificial neural network (ANN) based artificial intelligence (AI), that would enable it in the near future. Notably, such systems would have a number of specific advantages over biological life, such as the ability to pass acquired traits to offspring, significantly improved speed, accuracy, and redundancy of their genetic carrier, and potentially unlimited lifespans. Public blockchain-based dVMs provide an uncontained environment for the development of artificial general intelligence (AGI) with the capability to evolve by self-direction.
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Affiliation(s)
- Oleg Abramov
- Planetary Science Institute, 1700 E. Fort Lowell Rd., Suite 106, 85719-2395, Tucson, AZ, USA.
| | | | - Stephen J Mojzsis
- Origins Research Institute, Research Centre for Astronomy and Earth Sciences, 15-17 Konkoly Thege Miklós ut, Budapest, 1121, Hungary.,Department of Lithospheric Research, University Vienna, UZA 2, Althanstrasse 14, 1090, Vienna, Austria.,Department of Geological Sciences, University of Colorado at Boulder, 2200 Colorado Avenue UCB 399, 80309, Boulder, CO, USA
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72
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Burton S, Vicinanza D, Exell T, Newell KM, Irwin G, Williams GKR. Attractor dynamics of elite performance: the high bar longswing. Sports Biomech 2021:1-14. [PMID: 34309483 DOI: 10.1080/14763141.2021.1954236] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 11/14/2020] [Accepted: 07/06/2021] [Indexed: 10/20/2022]
Abstract
Combining biomechanics and motor control, the aim of this study was to investigate the limit cycle dynamics during the high bar longswing across the UK elite gymnastics pathway age groupings. Senior, junior and development gymnasts (N = 30) performed three sets of eight consecutive longswings on the high bar. The centre of mass motion was examined through Poincaré plots and recurrence quantification analysis exploring the limit cycle dynamics of the longswing. Close to one-dimensional limit cycles were displayed for the senior (correlation dimension (CD) = 1.17 ± .08), junior (CD = 1.26 ± .08) and development gymnasts (CD = 1.33 ± .14). Senior elite gymnasts displayed increased recurrence characteristics in addition to longer longswing duration (p < .01) and lower radial angular velocity of the mass centre (p < .01). All groups of gymnasts had highly recurrent and predictable limit cycle characteristics. The findings of this research support the postulation that the further practice, experience and individual development associated with the senior gymnasts contribute to the refinement of the longswing from a nonlinear dynamics perspective. These findings support the idea of functional task decomposition informing the understanding of skill and influencing coaches' decisions around skill development and physical preparation.
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Affiliation(s)
- Sophie Burton
- School of Sport and Health Sciences, Cardiff Metropolitan University, Cardiff, UK
| | - Domenico Vicinanza
- Department of Computing and Technology, Anglia Ruskin University, Cambridge, UK
| | - Timothy Exell
- School of Sport, Health and Exercise Science, University of Portsmouth, Portsmouth UK
| | - Karl M Newell
- Department of Kinesiology, University of Georgia, Athens, GA, USA
| | - Gareth Irwin
- School of Sport and Health Sciences, Cardiff Metropolitan University, Cardiff, UK
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73
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Roberts MG, Burgess S, Toombs-Ruane LJ, Benschop J, Marshall JC, French NP. Combining mutation and horizontal gene transfer in a within-host model of antibiotic resistance. Math Biosci 2021; 339:108656. [PMID: 34216634 DOI: 10.1016/j.mbs.2021.108656] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/25/2021] [Revised: 06/17/2021] [Accepted: 06/18/2021] [Indexed: 11/25/2022]
Abstract
Antibiotics are used extensively to control infections in humans and animals, usually by injection or a course of oral tablets. There are several methods by which bacteria can develop antimicrobial resistance (AMR), including mutation during DNA replication and plasmid mediated horizontal gene transfer (HGT). We present a model for the development of AMR within a single host animal. We derive criteria for a resistant mutant strain to replace the existing wild-type bacteria, and for co-existence of the wild-type and mutant. Where resistance develops through HGT via conjugation we derive criteria for the resistant strain to be excluded or co-exist with the wild-type. Our results are presented as bifurcation diagrams with thresholds determined by the relative fitness of the bacteria strains, expressed in terms of reproduction numbers. The results show that it is possible that applying and then relaxing antibiotic control may lead to the bacterial load returning to pre-control levels, but with an altered structure with regard to the variants that comprise the population. Removing antimicrobial selection pressure will not necessarily reduce AMR and, at a population level, other approaches to infection prevention and control are required, particularly when AMR is driven by both mutation and mobile genetic elements.
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Affiliation(s)
- M G Roberts
- School of Natural & Computational Sciences, Massey University, Private Bag 102 904, North Shore Mail Centre, Auckland, 0745, New Zealand; New Zealand Institute for Advanced Study, Massey University, Private Bag 102 904, North Shore Mail Centre, Auckland, 0745, New Zealand; Infectious Disease Research Centre, Massey University, Private Bag 11-222, Palmerston North, 4442, New Zealand.
| | - S Burgess
- Infectious Disease Research Centre, Massey University, Private Bag 11-222, Palmerston North, 4442, New Zealand; School of Veterinary Sciences, Massey University, Private Bag 11-222, Palmerston North, 4442, New Zealand; mEpilab, Massey University, Private Bag 11-222, Palmerston North, 4442, New Zealand
| | - L J Toombs-Ruane
- Infectious Disease Research Centre, Massey University, Private Bag 11-222, Palmerston North, 4442, New Zealand; School of Veterinary Sciences, Massey University, Private Bag 11-222, Palmerston North, 4442, New Zealand; mEpilab, Massey University, Private Bag 11-222, Palmerston North, 4442, New Zealand
| | - J Benschop
- Infectious Disease Research Centre, Massey University, Private Bag 11-222, Palmerston North, 4442, New Zealand; School of Veterinary Sciences, Massey University, Private Bag 11-222, Palmerston North, 4442, New Zealand; mEpilab, Massey University, Private Bag 11-222, Palmerston North, 4442, New Zealand
| | - J C Marshall
- Infectious Disease Research Centre, Massey University, Private Bag 11-222, Palmerston North, 4442, New Zealand; mEpilab, Massey University, Private Bag 11-222, Palmerston North, 4442, New Zealand; School of Fundamental Sciences, Massey University, Private Bag 11-222, Palmerston North, 4442, New Zealand
| | - N P French
- New Zealand Institute for Advanced Study, Massey University, Private Bag 102 904, North Shore Mail Centre, Auckland, 0745, New Zealand; Infectious Disease Research Centre, Massey University, Private Bag 11-222, Palmerston North, 4442, New Zealand; mEpilab, Massey University, Private Bag 11-222, Palmerston North, 4442, New Zealand; New Zealand Food Safety Science & Research Centre, Massey University, Private Bag 11-222, Palmerston North, 4442, New Zealand
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74
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Abstract
Infants' ability to coordinate their attention with other people develops profoundly across the first year of life. Mainly based on experimental research focusing on infants' behavior under highly controlled conditions, developmental milestones were identified and explained in the past by prominent theories in terms of the onset of specific cognitive skills. In contrast to this approach, recent longitudinal research challenges this perspective with findings suggesting that social attention develops continuously with a gradual refinement of skills. Informed by these findings, we argue for an interactionist and dynamical systems view that bases observable advances in infant social attention skills on increasingly fine-tuned mutual adjustments in the caregiver-infant dyad, resulting in gradually improving mutual prediction. We present evidence for this view from recent studies leveraging new technologies which afford the opportunity to dynamically track social interactions in real-time. These new technically-sophisticated studies offer unprecedented insights into the dynamic processes of infant-caregiver social attention. It is now possible to track in much greater detail fluctuations over time with regard to object-directed attention as well as social attention and how these processes relate to one another. Encouraged by these initial results and new insights from this interactionist developmental social neuroscience approach, we conclude with a "call to action" in which we advocate for more ecologically valid paradigms for studying social attention as a dynamic and bi-directional process.
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75
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Komar J, Ong CYY, Choo CZY, Chow JY. Perceptual-motor skill transfer: Multidimensionality and specificity of both general and specific transfers. Acta Psychol (Amst) 2021; 217:103321. [PMID: 33957573 DOI: 10.1016/j.actpsy.2021.103321] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/20/2020] [Revised: 03/31/2021] [Accepted: 04/23/2021] [Indexed: 10/21/2022] Open
Abstract
This paper aims to investigate perceptual-motor skill transfer, both through the specific as well as the general aspect of skill transfer. Specifically, we examined differences in skill transfer that occurred between participants who are skilled in practicing a perceptual motor activity involving striking with an implement and participants who are skilled in their own sports but are novice to striking task (i.e., batting an immobile ball). Skill transfer was assessed through the effect of practicing a new, novel task on the performance (ball velocity), intrinsic behavior (elbow and shoulder kinematic) as well as on the impetus for exploratory behavior (variability of elbow and shoulder kinematics) in the two groups of participants (n = 8 for each group), with reference to another group of expert participants (n = 8) for this batting task. Results showed that positive skill transfer was present and was multidimensional in the group of participants who have experience in using an implement in striking tasks. In addition, both specific transfer as well as general transfer were dependent on the task dynamics. More precisely, positive transfer was observed both through a sharing of similar movement patterns, an impetus for exploration and a direct transfer of performance in a novel task between groups who have experience in using an implement in striking tasks.
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76
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Abstract
Analyses of transient dynamics are critical to understanding infectious disease transmission and persistence. Identifying and predicting transients across scales, from within-host to community-level patterns, plays an important role in combating ongoing epidemics and mitigating the risk of future outbreaks. Moreover, greater emphases on non-asymptotic processes will enable timely evaluations of wildlife and human diseases and lead to improved surveillance efforts, preventive responses, and intervention strategies. Here, we explore the contributions of transient analyses in recent models spanning the fields of epidemiology, movement ecology, and parasitology. In addition to their roles in predicting epidemic patterns and endemic outbreaks, we explore transients in the contexts of pathogen transmission, resistance, and avoidance at various scales of the ecological hierarchy. Examples illustrate how (i) transient movement dynamics at the individual host level can modify opportunities for transmission events over time; (ii) within-host energetic processes often lead to transient dynamics in immunity, pathogen load, and transmission potential; (iii) transient connectivity between discrete populations in response to environmental factors and outbreak dynamics can affect disease spread across spatial networks; and (iv) increasing species richness in a community can provide transient protection to individuals against infection. Ultimately, we suggest that transient analyses offer deeper insights and raise new, interdisciplinary questions for disease research, consequently broadening the applications of dynamical models for outbreak preparedness and management. SUPPLEMENTARY INFORMATION The online version contains supplementary material available at 10.1007/s12080-021-00514-w.
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Affiliation(s)
- Yun Tao
- Intelligence Community Postdoctoral Research Fellowship Program, Department of Ecology, Evolution and Marine Biology, University of California, Santa Barbara, CA 93106 USA
| | - Jessica L. Hite
- School of Veterinary Medicine, Department of Pathobiological Sciences, University of Wisconsin, Madison, WI 53706 USA
| | - Kevin D. Lafferty
- Western Ecological Research Center at UCSB Marine Science Institute, U.S. Geological Survey, CA 93106 Santa Barbara, USA
| | - David J. D. Earn
- Department of Mathematics and Statistics, McMaster University, Hamilton, ON L8S 4K1 Canada
| | - Nita Bharti
- Department of Biology Center for Infectious Disease Dynamics, Penn State University, University Park, PA 16802 USA
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77
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Brooks J, Crone JC, Spangler DP. A physiological and dynamical systems model of stress. Int J Psychophysiol 2021; 166:83-91. [PMID: 34029625 DOI: 10.1016/j.ijpsycho.2021.05.005] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2021] [Revised: 05/05/2021] [Accepted: 05/10/2021] [Indexed: 12/30/2022]
Abstract
Stress responses vary drastically for a given set of stimuli, individuals, or points in time. A potential source of this variance that is not well characterized arises from the theory of stress as a dynamical system, which implies a complex, nonlinear relationship between environmental/situational inputs and the development/experience of stress. In this framework, stress vs. non-stress states exist as attractor basins in a physiologic phase space. Here, we develop a model of stress as a dynamical system by coupling closed loop physiologic control to a dynamic oscillator in an attractor landscape. By characterizing the evolution of this model through phase space, we demonstrate strong sensitivity to the parameters controlling the dynamics and demonstrate multiple features of stress responses found in current research, implying that these parameters may contribute to a significant source of variability observed in empiric stress research.
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Affiliation(s)
- Justin Brooks
- D-Prime, LLC, United States of America; University of Maryland, Baltimore County, Department of Computer Science and Electrical Engineering, United States of America
| | - Joshua C Crone
- CCDC-ARL, Computational and Information Sciences Directorate, United States of America
| | - Derek P Spangler
- The Pennsylvania State University, Department of Biobehavioral Health, United States of America.
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78
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Garcia M, Rouchy E. [Does the network approach in psychopathology entail the eclipse of the disorder?]. Encephale 2021:S0013-7006(21)00083-X. [PMID: 33994161 DOI: 10.1016/j.encep.2021.02.004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2020] [Revised: 01/15/2021] [Accepted: 02/01/2021] [Indexed: 11/22/2022]
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79
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Garbarino S, Lorenzi M. Investigating hypotheses of neurodegeneration by learning dynamical systems of protein propagation in the brain. Neuroimage 2021; 235:117980. [PMID: 33823273 DOI: 10.1016/j.neuroimage.2021.117980] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/07/2021] [Revised: 02/20/2021] [Accepted: 03/12/2021] [Indexed: 11/28/2022] Open
Abstract
We introduce a theoretical framework for estimating, comparing and interpreting mechanistic hypotheses on long term protein propagation across brain networks in neurodegenerative disorders (ND). The model is expressed within a Bayesian non-parametric regression setting, where mechanisms of protein dynamics are inferred by means of gradient matching on dynamical systems (DS). The Bayesian formalism, combined with stochastic variational inference, naturally allows for model comparison via assessment of model evidence, while providing uncertainty quantification of causal relationship underlying protein progressions. When applied to in-vivo AV45-PET brain imaging data measuring topographic amyloid deposition in Alzheimer's disease (AD), our model identified the mechanisms of accumulation, clearance and propagation as the best suited DS for bio-mechanical description of amyloid dynamics in AD, enabling realistic and accurate personalized simulation of amyloidosis.
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Affiliation(s)
- Sara Garbarino
- Universitè Côte d'Azur, Inria, Epione Research Project, France.
| | - Marco Lorenzi
- Universitè Côte d'Azur, Inria, Epione Research Project, France.
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- Universitè Côte d'Azur, Inria, Epione Research Project, France
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80
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Alicea B, Parent J, Singh U. Periodicity in the embryo: Emergence of order in space, diffusion of order in time. Biosystems 2021; 204:104405. [PMID: 33746021 DOI: 10.1016/j.biosystems.2021.104405] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/06/2021] [Revised: 03/07/2021] [Accepted: 03/08/2021] [Indexed: 02/02/2023]
Abstract
Does embryonic development exhibit characteristic temporal features? This is apparent in evolution, where evolutionary change has been shown to occur in bursts of activity. Using two animal models (Nematode, Caenorhabditis elegans and Zebrafish, Danio rerio) and simulated data, we demonstrate that temporal heterogeneity exists in embryogenesis at the cellular level, and may have functional consequences. Cell proliferation and division from cell tracking data is subject to analysis to characterize specific features in each model species. Simulated data is then used to understand what role this variation might play in producing phenotypic variation in the adult phenotype. This goes beyond a molecular characterization of developmental regulation to provide a quantitative result at the phenotypic scale of complexity.
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Affiliation(s)
- Bradly Alicea
- OpenWorm Foundation, Boston, MA, USA; Orthogonal Research and Education Laboratory, Champaign, IL, USA.
| | - Jesse Parent
- Orthogonal Research and Education Laboratory, Champaign, IL, USA
| | - Ujjwal Singh
- OpenWorm Foundation, Boston, MA, USA; IIIT Delhi, Delhi, India
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81
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Holden MH, Lockyer J. Poacher-population dynamics when legal trade of naturally deceased organisms funds anti-poaching enforcement. J Theor Biol 2021; 517:110618. [PMID: 33639137 DOI: 10.1016/j.jtbi.2021.110618] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2020] [Revised: 12/07/2020] [Accepted: 01/29/2021] [Indexed: 11/21/2022]
Abstract
Can a regulated, legal market for wildlife products protect species threatened by poaching? It is one of the most controversial ideas in biodiversity conservation. Perhaps the most convincing reason for legalizing wildlife trade is that trade revenue could fund the protection and conservation of poached species. In this paper, we examine the possible poacher-population dynamic consequences of legal trade funding conservation. The model consists of a manager scavenging carcasses for wildlife product, who then sells the product, and directs a portion of the revenue towards funding anti-poaching law enforcement. Through a global analysis of the model, we derive the critical proportion of product the manager must scavenge, and the critical proportion of trade revenue the manager must allocate towards increased enforcement, in order for legal trade to lead to abundant long-term wildlife populations. We illustrate how the model could inform management with parameter values derived from the African elephant literature, under a hypothetical scenario where a manager scavenges elephant carcasses to sell ivory. We find that there is a large region of parameter space where populations go extinct under legal trade unless a significant portion of trade revenue is directed towards protecting populations from poaching. The model is general and therefore can be used as a starting point for exploring the consequences of funding many conservation programs using wildlife trade revenue.
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82
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Villota-Narvaez Y, Garzon-Alvarado DA, Ramirez-Martinez AM. A dynamical system for the IGF1-AKT signaling pathway in skeletal muscle adaptation. Biosystems 2021; 202:104355. [PMID: 33453318 DOI: 10.1016/j.biosystems.2021.104355] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/14/2020] [Revised: 12/14/2020] [Accepted: 01/05/2021] [Indexed: 11/16/2022]
Abstract
Physical activity produces a change in skeletal-muscle size by activating synthesis or degradation of protein, which are outcomes of stimulating the IGF1-AKT signaling pathway. In this work, we propose a mathematical model that predicts the variation in muscle size under different activity conditions. The IGF1-AKT pathway was modeled using its 4 main molecules as variables in a dynamical system. We checked the stability of the system; we defined exercise training as a function of intensity, duration, and frequency; and we tested the model under four scenarios: first, we considered the daily low-intensity activity that should not promote atrophy nor hypertrophy (steady state); second, we simulated the effects of physical therapy in spinal cord injury patients (atrophy); third, we simulated exercise training in healthy subjects (hypertrophy); and fourth, we considered the effects of suspending a training program in healthy subjects (recovery after hypertrophy). Results showed that: protein synthesis and degradation are inactive, thus the size of the muscle stays stable in the first scenario; the muscle decreases only 10% of its initial size after 84 days of therapy every two days in the second scenario; training frequency produces rapid hypertrophy (11% after 25 days) when training every day, to no hypertrophy when training every 5 days in the third scenario; and a reduction of 50% the gain of the training program in the fourth scenario. By comparing our results to experimental reports, we found a remarkable agreement; therefore, our model is suitable for the development of training and therapeutic protocols.
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Affiliation(s)
- Yesid Villota-Narvaez
- Biomimetics Laboratory, Instituto de Biotecnología (IBUN), and Numerical Methods and Modeling Research Group (GNUM), Universidad Nacional de Colombia, Bogotá, Colombia.
| | - Diego A Garzon-Alvarado
- Biomimetics Laboratory, Instituto de Biotecnología (IBUN), and Numerical Methods and Modeling Research Group (GNUM), Universidad Nacional de Colombia, Bogotá, Colombia; Computational Modeling of Natural Systems Research Group (COMMONS), Mechanical Engineering Department, Universidad Central, Bogotá, Colombia.
| | - Angelica M Ramirez-Martinez
- Biomimetics Laboratory, Instituto de Biotecnología (IBUN), and Numerical Methods and Modeling Research Group (GNUM), Universidad Nacional de Colombia, Bogotá, Colombia; Computational Modeling of Natural Systems Research Group (COMMONS), Mechanical Engineering Department, Universidad Central, Bogotá, Colombia; Biomedical Engineering Department, Engineering Faculty, Universidad Militar Nueva Granada, Bogotá, Colombia.
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83
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Ballesteros A, Blasco A, Gutierrez-Sagredo I. Hamiltonian structure of compartmental epidemiological models. Physica D 2020; 413:132656. [PMID: 32834251 PMCID: PMC7375975 DOI: 10.1016/j.physd.2020.132656] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2020] [Revised: 07/17/2020] [Accepted: 07/18/2020] [Indexed: 05/09/2023]
Abstract
Any epidemiological compartmental model with constant population is shown to be a Hamiltonian dynamical system in which the total population plays the role of the Hamiltonian function. Moreover, some particular cases within this large class of models are shown to be bi-Hamiltonian. New interacting compartmental models among different populations, which are endowed with a Hamiltonian structure, are introduced. The Poisson structures underlying the Hamiltonian description of all these dynamical systems are explicitly presented, and their associated Casimir functions are shown to provide an efficient tool in order to find exact analytical solutions for epidemiological models, such as the ones describing the dynamics of the COVID-19 pandemic.
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Affiliation(s)
| | - Alfonso Blasco
- Departamento de Física, Universidad de Burgos, 09001 Burgos, Spain
| | - Ivan Gutierrez-Sagredo
- Departamento de Física, Universidad de Burgos, 09001 Burgos, Spain
- Departamento de Matemáticas y Computación, Universidad de Burgos, 09001 Burgos, Spain
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84
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Rajendra P, Brahmajirao V. Modeling of dynamical systems through deep learning. Biophys Rev 2020; 12:10.1007/s12551-020-00776-4. [PMID: 33222032 PMCID: PMC7755960 DOI: 10.1007/s12551-020-00776-4] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2020] [Accepted: 11/08/2020] [Indexed: 12/18/2022] Open
Abstract
This review presents a modern perspective on dynamical systems in the context of current goals and open challenges. In particular, our review focuses on the key challenges of discovering dynamics from data and finding data-driven representations that make nonlinear systems amenable to linear analysis. We explore various challenges in modern dynamical systems, along with emerging techniques in data science and machine learning to tackle them. The two chief challenges are (1) nonlinear dynamics and (2) unknown or partially known dynamics. Machine learning is providing new and powerful techniques for both challenges. Dimensionality reduction methods are used for projecting dynamical methods in reduced form, and these methods perform computational efficiency on real-world data. Data-driven models drive to discover the governing equations and give laws of physics. The identification of dynamical systems through deep learning techniques succeeds in inferring physical systems. Machine learning provides advanced new and powerful algorithms for nonlinear dynamics. Advanced deep learning methods like autoencoders, recurrent neural networks, convolutional neural networks, and reinforcement learning are used in modeling of dynamical systems.
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Affiliation(s)
- P Rajendra
- Department of Mathematics CMR Institute of Technology, Bengaluru, India.
| | - V Brahmajirao
- School of Biotechnology MGNIRSA, D.S.R. Foundation, Hyderabad, India
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85
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Cheng X, D'Orsogna MR, Chou T. Mathematical modeling of depressive disorders: Circadian driving, bistability and dynamical transitions. Comput Struct Biotechnol J 2020; 19:664-690. [PMID: 33510869 PMCID: PMC7815682 DOI: 10.1016/j.csbj.2020.10.035] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2020] [Revised: 10/30/2020] [Accepted: 10/30/2020] [Indexed: 11/30/2022] Open
Abstract
The hypothalamus-pituitary-adrenal (HPA) axis is a key neuroendocrine system implicated in stress response, major depression disorder, and post-traumatic stress disorder. We present a new, compact dynamical systems model for the response of the HPA axis to external stimuli, representing stressors or therapeutic intervention, in the presence of a circadian input. Our work builds upon previous HPA axis models where hormonal dynamics are separated into slow and fast components. Several simplifications allow us to derive an effective model of two equations, similar to a multiplicative-input FitzHugh-Nagumo system, where two stable states, a healthy and a diseased one, arise. We analyze the effective model in the context of state transitions driven by external shocks to the hypothalamus, but also modulated by circadian rhythms. Our analyses provide mechanistic insight into the effects of the circadian cycle on input driven transitions of the HPA axis and suggest a circadian influence on exposure or cognitive behavioral therapy in depression, or post-traumatic stress disorder treatment.
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Affiliation(s)
- Xiaoou Cheng
- School of Mathematical Sciences, Peking University, Haidian District, Beijing 100871, China
| | - Maria R D'Orsogna
- Dept. of Mathematics, California State University, Northridge, CA 91330, United States
- Dept. of Computational Medicine, UCLA, Los Angeles, CA 90095, United States
| | - Tom Chou
- Dept. of Computational Medicine, UCLA, Los Angeles, CA 90095, United States
- Dept. of Mathematics, UCLA, Los Angeles, CA 90095, United States
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86
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Piazzola C, Tamellini L, Tempone R. A note on tools for prediction under uncertainty and identifiability of SIR-like dynamical systems for epidemiology. Math Biosci 2020; 332:108514. [PMID: 33217409 DOI: 10.1016/j.mbs.2020.108514] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/04/2020] [Revised: 11/09/2020] [Accepted: 11/09/2020] [Indexed: 12/18/2022]
Abstract
We provide an overview of the methods that can be used for prediction under uncertainty and data fitting of dynamical systems, and of the fundamental challenges that arise in this context. The focus is on SIR-like models, that are being commonly used when attempting to predict the trend of the COVID-19 pandemic. In particular, we raise a warning flag about identifiability of the parameters of SIR-like models; often, it might be hard to infer the correct values of the parameters from data, even for very simple models, making it non-trivial to use these models for meaningful predictions. Most of the points that we touch upon are actually generally valid for inverse problems in more general setups.
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Affiliation(s)
- Chiara Piazzola
- Consiglio Nazionale delle Ricerche - Istituto di Matematica Applicata e Tecnologie Informatiche "E. Magenes" (CNR-IMATI), Via Ferrata 5/A, 27100 Pavia, Italy.
| | - Lorenzo Tamellini
- Consiglio Nazionale delle Ricerche - Istituto di Matematica Applicata e Tecnologie Informatiche "E. Magenes" (CNR-IMATI), Via Ferrata 5/A, 27100 Pavia, Italy.
| | - Raúl Tempone
- Alexander von Humboldt Professor in Mathematics for Uncertainty Quantification, RWTH Aachen University, Pontdriesch 14-16, 52062, Aachen, Germany; King Abdullah University of Science and Technology (KAUST) - Computer, Electrical and Mathematical Sciences & Engineering Division (CEMSE), Thuwal, 23955-6900, Saudi Arabia.
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87
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Lei C, Wang Y, Zhao J, Li K, Jiang H, Wang Q. A patient specific forecasting model for human albumin based on deep neural networks. Comput Methods Programs Biomed 2020; 196:105555. [PMID: 32544776 DOI: 10.1016/j.cmpb.2020.105555] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/09/2020] [Revised: 05/06/2020] [Accepted: 05/16/2020] [Indexed: 06/11/2023]
Abstract
BACKGROUND AND OBJECTIVES Hypoalbuminemia can be life threatening among critically ill patients. In this study, we develop a patient-specific monitoring and forecasting model based on deep neural networks to predict concentrations of albumin and a set of selected biochemical markers for critically ill patients in real-time. METHODS Under the assumption that metabolism of a patient follows a patient-specific dynamical process that can be determined from sufficient prior data taken from the patient, we apply a machine learning method to develop the patient-specific model for a critically ill, poly-trauma patient. Six representative biochemical markers (albumin (ALB), creatinine (Cr), osmotic pressure (OSM), alanine aminotransferase (ALT), total bilirubin (TB), direct bilirubin (DB)) were collected from the patient while scheduled exogenous albumin injection was administered to the patient for the total of 27 consecutive days. A sliding window of data in 11 consecutive days were used to train and test the neural networks in the model. RESULTS The obtained dynamical system model represented by neural networks is used to forecast the biochemical markers of the patient in the next 24 h. The relative error between the predictions and the clinical data remains consistently lower than 2%. CONCLUSIONS This study demonstrates that a patient-specific dynamical system model can be established to monitor and forecast dynamical behavior of concentrations of patients' biochemical markers (including albumin) using deep learning methods on neural networks.
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Affiliation(s)
- Cheng Lei
- Beijing Computational Science Research Center, Beijing 100193, China
| | - Yu Wang
- Institute for Emergency and Disaster Medicine, Sichuan Academy of Medical Sciences, Sichuan Provincial People's Hospital, School of Medicine, University of Electronic Science and Technology of China, Chengdu 610072, Sichuan, China
| | - Jia Zhao
- Department of Mathematics and Statistics, Utah State University, Logan, UT 84322, USA
| | - Kexun Li
- Institute for Emergency and Disaster Medicine, Sichuan Academy of Medical Sciences, Sichuan Provincial People's Hospital, School of Medicine, University of Electronic Science and Technology of China, Chengdu 610072, Sichuan, China
| | - Hua Jiang
- Institute for Emergency and Disaster Medicine, Sichuan Academy of Medical Sciences, Sichuan Provincial People's Hospital, School of Medicine, University of Electronic Science and Technology of China, Chengdu 610072, Sichuan, China.
| | - Qi Wang
- Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA.
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88
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Abstract
This work is motivated by the following question in data-driven study of dynamical systems: given a dynamical system that is observed via time series of persistence diagrams that encode topological features of snapshots of solutions, what conclusions can be drawn about solutions of the original dynamical system? We address this challenge in the context of an N dimensional system of ordinary differential equation defined in \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$${\mathbb {R}}^N$$\end{document}RN. To each point in \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$${\mathbb {R}}^N$$\end{document}RN (e.g. an initial condition) we associate a persistence diagram. The main result of this paper is that under this association the preimage of every persistence diagram is contractible. As an application we provide conditions under which multiple time series of persistence diagrams can be used to conclude the existence of a fixed point of the differential equation that generates the time series.
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Affiliation(s)
- Jacek Cyranka
- Department of Mathematics, Rutgers, The State University of New Jersey, 110 Frelinghusen Rd., Piscataway, NJ 08854-8019 USA.,Institute of Informatics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland
| | - Konstantin Mischaikow
- Department of Mathematics, Rutgers, The State University of New Jersey, 110 Frelinghusen Rd., Piscataway, NJ 08854-8019 USA
| | - Charles Weibel
- Department of Mathematics, Rutgers, The State University of New Jersey, 110 Frelinghusen Rd., Piscataway, NJ 08854-8019 USA
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89
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Zhang X, Chong KH, Zhu L, Zheng J. A Monte Carlo method for in silico modeling and visualization of Waddington's epigenetic landscape with intermediate details. Biosystems 2020; 198:104275. [PMID: 33080349 DOI: 10.1016/j.biosystems.2020.104275] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2020] [Revised: 10/08/2020] [Accepted: 10/10/2020] [Indexed: 12/13/2022]
Abstract
Waddington's epigenetic landscape is a classic metaphor for describing the cellular dynamics during the development modulated by gene regulation. Quantifying Waddington's epigenetic landscape by mathematical modeling would be useful for understanding the mechanisms of cell fate determination. A few computational methods have been proposed for quantitative modeling of landscape; however, to model and visualize the landscape of a high dimensional gene regulatory system with realistic details is still challenging. Here, we propose a Monte Carlo method for modeling the Waddington's epigenetic landscape of a gene regulatory network (GRN). The method estimates the probability distribution of cellular states by collecting a large number of time-course simulations with random initial conditions. By projecting all the trajectories into a 2-dimensional plane of dimensions i and j, we can approximately calculate the quasi-potential U(xi,xj,∗)=-ln P(xi,xj,∗), where P(xi,xj,∗) is the estimated probability of an equilibrium steady state or a non-equilibrium state. Compared to the state-of-the-art methods, our Monte Carlo method can quantify the global potential landscape (or emergence behavior) of GRN for a high dimensional system. The potential landscapes show that not only attractors represent stability, but the paths between attractors are also part of the stability or robustness of biological systems. We demonstrate the novelty and reliability of our method by plotting the potential landscapes of a few published models of GRN.
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Affiliation(s)
- Xiaomeng Zhang
- Biomedical Informatics Lab, School of Computer Science and Engineering, Nanyang Technological University, 639798, Singapore
| | - Ket Hing Chong
- Biomedical Informatics Lab, School of Computer Science and Engineering, Nanyang Technological University, 639798, Singapore
| | - Lin Zhu
- School of Information Science and Technology, ShanghaiTech University, Pudong District, Shanghai 201210, China
| | - Jie Zheng
- School of Information Science and Technology, ShanghaiTech University, Pudong District, Shanghai 201210, China.
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90
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Ebrahimi A, Nowzari-Dalini A, Jalili M, Masoudi-Nejad A. Target controllability with minimal mediators in complex biological networks. Genomics 2020; 112:4938-4944. [PMID: 32905831 DOI: 10.1016/j.ygeno.2020.09.003] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/28/2020] [Revised: 08/27/2020] [Accepted: 09/03/2020] [Indexed: 01/02/2023]
Abstract
Controllability of a complex network system is related to finding a set of minimum number of nodes, known as drivers, controlling which allows having a full control on the dynamics of the network. For some applications, only a portion of the network is required to be controlled, for which target control has been proposed. Often, along the controlling route from driver nodes to target nodes, some mediators (intermediate nodes) are also unwillingly controlled, which might cause various side effects. In controlling cancerous cells, unwillingly controlling healthy cells, might result in weakening them, thus affecting the immune system against cancer. This manuscript proposes a suitable candidate solution to the problem of finding minimum number of driver nodes under minimal mediators. Although many others have attempted to develop algorithms to find minimum number of drivers for target control, the newly proposed algorithm is the first one that is capable of achieving this goal and at the same time, keeping the number of the mediators to a minimum. The proposed controllability condition, based on path lengths between node pairs, meets Kalman's controllability rank condition and can be applied on directed networks. Our results show that the path length is a major determinant of in properties of the target control under minimal mediators. As the average path length becomes larger, the ratio of drivers to target nodes decreases and the ratio of mediators to targets increases. The proposed methodology has potential applications in biological networks. The source code of the algorithm and the networks that have been used are available from the following link: https://github.com/LBBSoft/Target-Control-with-Minimal-Mediators.git.
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Affiliation(s)
- Ali Ebrahimi
- Laboratory of Systems Biology and Bioinformatics (LBB), Institute of Biochemistry and Biophysics, University of Tehran, Tehran, Iran
| | | | - Mahdi Jalili
- School of Engineering, RMIT University, Melbourne, Australia.
| | - Ali Masoudi-Nejad
- Laboratory of Systems Biology and Bioinformatics (LBB), Institute of Biochemistry and Biophysics, University of Tehran, Tehran, Iran.
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91
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Jin P, Zhang Z, Zhu A, Tang Y, Karniadakis GE. SympNets: Intrinsic structure-preserving symplectic networks for identifying Hamiltonian systems. Neural Netw 2020; 132:166-179. [PMID: 32890788 DOI: 10.1016/j.neunet.2020.08.017] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2020] [Revised: 07/12/2020] [Accepted: 08/17/2020] [Indexed: 10/23/2022]
Abstract
We propose new symplectic networks (SympNets) for identifying Hamiltonian systems from data based on a composition of linear, activation and gradient modules. In particular, we define two classes of SympNets: the LA-SympNets composed of linear and activation modules, and the G-SympNets composed of gradient modules. Correspondingly, we prove two new universal approximation theorems that demonstrate that SympNets can approximate arbitrary symplectic maps based on appropriate activation functions. We then perform several experiments including the pendulum, double pendulum and three-body problems to investigate the expressivity and the generalization ability of SympNets. The simulation results show that even very small size SympNets can generalize well, and are able to handle both separable and non-separable Hamiltonian systems with data points resulting from short or long time steps. In all the test cases, SympNets outperform the baseline models, and are much faster in training and prediction. We also develop an extended version of SympNets to learn the dynamics from irregularly sampled data. This extended version of SympNets can be thought of as a universal model representing the solution to an arbitrary Hamiltonian system.
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Affiliation(s)
- Pengzhan Jin
- LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China; School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Zhen Zhang
- Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
| | - Aiqing Zhu
- LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China; School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Yifa Tang
- LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China; School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China.
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92
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Kantner M, Koprucki T. Beyond just "flattening the curve": Optimal control of epidemics with purely non-pharmaceutical interventions. J Math Ind 2020; 10:23. [PMID: 32834921 DOI: 10.1186/s13362-020-0069-4] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/23/2020] [Accepted: 08/06/2020] [Indexed: 05/24/2023]
Abstract
When effective medical treatment and vaccination are not available, non-pharmaceutical interventions such as social distancing, home quarantine and far-reaching shutdown of public life are the only available strategies to prevent the spread of epidemics. Based on an extended SEIR (susceptible-exposed-infectious-recovered) model and continuous-time optimal control theory, we compute the optimal non-pharmaceutical intervention strategy for the case that a vaccine is never found and complete containment (eradication of the epidemic) is impossible. In this case, the optimal control must meet competing requirements: First, the minimization of disease-related deaths, and, second, the establishment of a sufficient degree of natural immunity at the end of the measures, in order to exclude a second wave. Moreover, the socio-economic costs of the intervention shall be kept at a minimum. The numerically computed optimal control strategy is a single-intervention scenario that goes beyond heuristically motivated interventions and simple "flattening of the curve". Careful analysis of the computed control strategy reveals, however, that the obtained solution is in fact a tightrope walk close to the stability boundary of the system, where socio-economic costs and the risk of a new outbreak must be constantly balanced against one another. The model system is calibrated to reproduce the initial exponential growth phase of the COVID-19 pandemic in Germany.
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Affiliation(s)
- Markus Kantner
- Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Mohrenstr. 39, Berlin, 10117 Germany
| | - Thomas Koprucki
- Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Mohrenstr. 39, Berlin, 10117 Germany
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93
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Abstract
While the spatial topological persistence is naturally constructed from a radius-based filtration, it has hardly been derived from a temporal filtration. Most topological models are designed for the global topology of a given object as a whole. There is no method reported in the literature for the topology of an individual component in an object to the best of our knowledge. For many problems in science and engineering, the topology of an individual component is important for describing its properties. We propose evolutionary homology (EH) constructed via a time evolution-based filtration and topological persistence. Our approach couples a set of dynamical systems or chaotic oscillators by the interactions of a physical system, such as a macromolecule. The interactions are approximated by weighted graph Laplacians. Simplices, simplicial complexes, algebraic groups and topological persistence are defined on the coupled trajectories of the chaotic oscillators. The resulting EH gives rise to time-dependent topological invariants or evolutionary barcodes for an individual component of the physical system, revealing its topology-function relationship. In conjunction with Wasserstein metrics, the proposed EH is applied to protein flexibility analysis, an important problem in computational biophysics. Numerical results for the B-factor prediction of a benchmark set of 364 proteins indicate that the proposed EH outperforms all the other state-of-the-art methods in the field.
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Affiliation(s)
- Zixuan Cang
- Department of Mathematics, Michigan State University
| | - Elizabeth Munch
- Department of Computational Mathematics, Science and Engineering, Michigan State University
| | - Guo-Wei Wei
- Department of Mathematics, Michigan State University
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94
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Abstract
BACKGROUND A growing body of research highlights the limitations of traditional methods for studying the process of change in psychotherapy. The science of complex systems offers a useful paradigm for studying patterns of psychopathology and the development of more functional patterns in psychotherapy. Some basic principles of change are presented from subdisciplines of complexity science that are particularly relevant to psychotherapy: dynamical systems theory, synergetics, and network theory. Two early warning signs of system transition that have been identified across sciences (critical fluctuations and critical slowing) are also described. The network destabilization and transition (NDT) model of therapeutic change is presented as a conceptual framework to import these principles to psychotherapy research and to suggest future research directions. DISCUSSION A complex systems approach has a number of implications for psychotherapy research. We describe important design considerations, targets for research, and analytic tools that can be used to conduct this type of research. CONCLUSIONS A complex systems approach to psychotherapy research is both viable and necessary to more fully capture the dynamics of human change processes. Research to date suggests that the process of change in psychotherapy can be nonlinear and that periods of increased variability and critical slowing might be early warning signals of transition in psychotherapy, as they are in other systems in nature. Psychotherapy research has been limited by small samples and infrequent assessment, but ambulatory and electronic methods now allow researchers to more fully realize the potential of concepts and methods from complexity science.
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Affiliation(s)
- Adele M Hayes
- Department of Psychological and Brain Sciences, University of Delaware, 108 Wolf Hall, Newark, DE, 19716, USA.
| | - Leigh A Andrews
- Department of Psychological and Brain Sciences, University of Delaware, 108 Wolf Hall, Newark, DE, 19716, USA
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95
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Pontes-Filho S, Lind P, Yazidi A, Zhang J, Hammer H, Mello GBM, Sandvig I, Tufte G, Nichele S. A neuro-inspired general framework for the evolution of stochastic dynamical systems: Cellular automata, random Boolean networks and echo state networks towards criticality. Cogn Neurodyn 2020; 14:657-74. [PMID: 33014179 DOI: 10.1007/s11571-020-09600-x] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/30/2019] [Revised: 05/08/2020] [Accepted: 05/14/2020] [Indexed: 10/27/2022] Open
Abstract
Although deep learning has recently increased in popularity, it suffers from various problems including high computational complexity, energy greedy computation, and lack of scalability, to mention a few. In this paper, we investigate an alternative brain-inspired method for data analysis that circumvents the deep learning drawbacks by taking the actual dynamical behavior of biological neural networks into account. For this purpose, we develop a general framework for dynamical systems that can evolve and model a variety of substrates that possess computational capacity. Therefore, dynamical systems can be exploited in the reservoir computing paradigm, i.e., an untrained recurrent nonlinear network with a trained linear readout layer. Moreover, our general framework, called EvoDynamic, is based on an optimized deep neural network library. Hence, generalization and performance can be balanced. The EvoDynamic framework contains three kinds of dynamical systems already implemented, namely cellular automata, random Boolean networks, and echo state networks. The evolution of such systems towards a dynamical behavior, called criticality, is investigated because systems with such behavior may be better suited to do useful computation. The implemented dynamical systems are stochastic and their evolution with genetic algorithm mutates their update rules or network initialization. The obtained results are promising and demonstrate that criticality is achieved. In addition to the presented results, our framework can also be utilized to evolve the dynamical systems connectivity, update and learning rules to improve the quality of the reservoir used for solving computational tasks and physical substrate modeling.
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96
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Burger J, van der Veen DC, Robinaugh DJ, Quax R, Riese H, Schoevers RA, Epskamp S. Bridging the gap between complexity science and clinical practice by formalizing idiographic theories: a computational model of functional analysis. BMC Med 2020. [PMID: 32264914 DOI: 10.31234/osf.io/gw2uc] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 05/08/2023] Open
Abstract
BACKGROUND The past decades of research have seen an increase in statistical tools to explore the complex dynamics of mental health from patient data, yet the application of these tools in clinical practice remains uncommon. This is surprising, given that clinical reasoning, e.g., case conceptualizations, largely coincides with the dynamical system approach. We argue that the gap between statistical tools and clinical practice can partly be explained by the fact that current estimation techniques disregard theoretical and practical considerations relevant to psychotherapy. To address this issue, we propose that case conceptualizations should be formalized. We illustrate this approach by introducing a computational model of functional analysis, a framework commonly used by practitioners to formulate case conceptualizations and design patient-tailored treatment. METHODS We outline the general approach of formalizing idiographic theories, drawing on the example of a functional analysis for a patient suffering from panic disorder. We specified the system using a series of differential equations and simulated different scenarios; first, we simulated data without intervening in the system to examine the effects of avoidant coping on the development of panic symptomatic. Second, we formalized two interventions commonly used in cognitive behavioral therapy (CBT; exposure and cognitive reappraisal) and subsequently simulated their effects on the system. RESULTS The first simulation showed that the specified system could recover several aspects of the phenomenon (panic disorder), however, also showed some incongruency with the nature of panic attacks (e.g., rapid decreases were not observed). The second simulation study illustrated differential effects of CBT interventions for this patient. All tested interventions could decrease panic levels in the system. CONCLUSIONS Formalizing idiographic theories is promising in bridging the gap between complexity science and clinical practice and can help foster more rigorous scientific practices in psychotherapy, through enhancing theory development. More precise case conceptualizations could potentially improve intervention planning and treatment outcomes. We discuss applications in psychotherapy and future directions, amongst others barriers for systematic theory evaluation and extending the framework to incorporate interactions between individual systems, relevant for modeling social learning processes. With this report, we hope to stimulate future efforts in formalizing clinical frameworks.
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Affiliation(s)
- Julian Burger
- University of Groningen, University Medical Center Groningen, University Center Psychiatry (UCP) Interdisciplinary Center Psychopathology and Emotion Regulation (ICPE), Hanzeplein 1, 9713 GZ, Groningen, The Netherlands.
- University of Amsterdam, Institute for Advanced Study, Amsterdam, The Netherlands.
| | - Date C van der Veen
- University of Groningen, University Medical Center Groningen, University Center Psychiatry (UCP) Interdisciplinary Center Psychopathology and Emotion Regulation (ICPE), Hanzeplein 1, 9713 GZ, Groningen, The Netherlands
| | - Donald J Robinaugh
- Harvard University, Department of Psychiatry, Massachusetts General Hospital, .Cambridge, MA, USA
| | - Rick Quax
- University of Amsterdam, Institute for Advanced Study, Amsterdam, The Netherlands
| | - Harriëtte Riese
- University of Groningen, University Medical Center Groningen, University Center Psychiatry (UCP) Interdisciplinary Center Psychopathology and Emotion Regulation (ICPE), Hanzeplein 1, 9713 GZ, Groningen, The Netherlands
| | - Robert A Schoevers
- University of Groningen, University Medical Center Groningen, University Center Psychiatry (UCP) Interdisciplinary Center Psychopathology and Emotion Regulation (ICPE), Hanzeplein 1, 9713 GZ, Groningen, The Netherlands
| | - Sacha Epskamp
- University of Amsterdam, Institute for Advanced Study, Amsterdam, The Netherlands
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97
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Burger J, van der Veen DC, Robinaugh DJ, Quax R, Riese H, Schoevers RA, Epskamp S. Bridging the gap between complexity science and clinical practice by formalizing idiographic theories: a computational model of functional analysis. BMC Med 2020; 18:99. [PMID: 32264914 PMCID: PMC7333286 DOI: 10.1186/s12916-020-01558-1] [Citation(s) in RCA: 34] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 10/11/2019] [Accepted: 03/16/2020] [Indexed: 12/18/2022] Open
Abstract
BACKGROUND The past decades of research have seen an increase in statistical tools to explore the complex dynamics of mental health from patient data, yet the application of these tools in clinical practice remains uncommon. This is surprising, given that clinical reasoning, e.g., case conceptualizations, largely coincides with the dynamical system approach. We argue that the gap between statistical tools and clinical practice can partly be explained by the fact that current estimation techniques disregard theoretical and practical considerations relevant to psychotherapy. To address this issue, we propose that case conceptualizations should be formalized. We illustrate this approach by introducing a computational model of functional analysis, a framework commonly used by practitioners to formulate case conceptualizations and design patient-tailored treatment. METHODS We outline the general approach of formalizing idiographic theories, drawing on the example of a functional analysis for a patient suffering from panic disorder. We specified the system using a series of differential equations and simulated different scenarios; first, we simulated data without intervening in the system to examine the effects of avoidant coping on the development of panic symptomatic. Second, we formalized two interventions commonly used in cognitive behavioral therapy (CBT; exposure and cognitive reappraisal) and subsequently simulated their effects on the system. RESULTS The first simulation showed that the specified system could recover several aspects of the phenomenon (panic disorder), however, also showed some incongruency with the nature of panic attacks (e.g., rapid decreases were not observed). The second simulation study illustrated differential effects of CBT interventions for this patient. All tested interventions could decrease panic levels in the system. CONCLUSIONS Formalizing idiographic theories is promising in bridging the gap between complexity science and clinical practice and can help foster more rigorous scientific practices in psychotherapy, through enhancing theory development. More precise case conceptualizations could potentially improve intervention planning and treatment outcomes. We discuss applications in psychotherapy and future directions, amongst others barriers for systematic theory evaluation and extending the framework to incorporate interactions between individual systems, relevant for modeling social learning processes. With this report, we hope to stimulate future efforts in formalizing clinical frameworks.
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Affiliation(s)
- Julian Burger
- University of Groningen, University Medical Center Groningen, University Center Psychiatry (UCP) Interdisciplinary Center Psychopathology and Emotion Regulation (ICPE), Hanzeplein 1, 9713 GZ, Groningen, The Netherlands.
- University of Amsterdam, Institute for Advanced Study, Amsterdam, The Netherlands.
| | - Date C van der Veen
- University of Groningen, University Medical Center Groningen, University Center Psychiatry (UCP) Interdisciplinary Center Psychopathology and Emotion Regulation (ICPE), Hanzeplein 1, 9713 GZ, Groningen, The Netherlands
| | - Donald J Robinaugh
- Harvard University, Department of Psychiatry, Massachusetts General Hospital, .Cambridge, MA, USA
| | - Rick Quax
- University of Amsterdam, Institute for Advanced Study, Amsterdam, The Netherlands
| | - Harriëtte Riese
- University of Groningen, University Medical Center Groningen, University Center Psychiatry (UCP) Interdisciplinary Center Psychopathology and Emotion Regulation (ICPE), Hanzeplein 1, 9713 GZ, Groningen, The Netherlands
| | - Robert A Schoevers
- University of Groningen, University Medical Center Groningen, University Center Psychiatry (UCP) Interdisciplinary Center Psychopathology and Emotion Regulation (ICPE), Hanzeplein 1, 9713 GZ, Groningen, The Netherlands
| | - Sacha Epskamp
- University of Amsterdam, Institute for Advanced Study, Amsterdam, The Netherlands
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98
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Ueda KI, Nishiura Y, Kitajo K. Mathematical mechanism of state-dependent phase resetting properties of alpha rhythm in the human brain. Neurosci Res 2020; 156:237-244. [PMID: 32197945 DOI: 10.1016/j.neures.2020.03.007] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2019] [Revised: 01/05/2020] [Accepted: 01/15/2020] [Indexed: 10/24/2022]
Abstract
It is well-known that 10-Hz alpha oscillations in humans observed by electroencephalogram (EEG) are enhanced when the eyes are closed. Toward explaining this, a previous experimental study using manipulation by transcranial magnetic stimulation (TMS) revealed more global propagation of phase resetting in the eyes-open condition than in the eyes-closed condition in the alpha band. Those results indicate a significant increase of directed information flow across brain networks from the stimulated area to the rest of the brain when the eyes are open, suggesting that sensitivity to environmental changes and external stimuli is adaptively controlled by changing the dynamics of the alpha rhythm. However, the mathematical mechanism mediating the changes in the sensitivity has not been well elucidated. In this study, we propose a qualitative mathematical model that describes the characteristic behavior of the EEG phase dynamics. Numerically, we find that the propagation properties of the phase resetting qualitatively depend on whether the population of oscillators at the stimulated area are synchronized. These results support the hypothesis that the dynamics of the alpha oscillations controls sensitivity to external stimuli.
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Affiliation(s)
- Kei-Ichi Ueda
- Graduate School of Science and Engineering, University of Toyama, Toyama-shi, Toyama 930-8555, Japan.
| | - Yasumasa Nishiura
- Research Institute for Electronic Science, Hokkaido Univesity, Sapporo, 060-0812 and MathAM-OIL, Tohoku University and AIST, Sendai, 980-8577, Japan
| | - Keiichi Kitajo
- RIKEN, CBS-TOYOTA Collaboration Center; RIKEN Center for Brain Science, Wako, Saitama 351-0198, Japan; Division of Neural Dynamics, Department of System Neuroscience, National Institute for Physiological Sciences, National Institutes of Natural Sciences, Okazaki, Aichi 444-8585, Japan; Department of Physiological Sciences, School of Life Science, The Graduate University for Advanced Studies (SOKENDAI), Okazaki, Aichi 444-8585, Japan
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99
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Burrows DRW, Samarut É, Liu J, Baraban SC, Richardson MP, Meyer MP, Rosch RE. Imaging epilepsy in larval zebrafish. Eur J Paediatr Neurol 2020; 24:70-80. [PMID: 31982307 PMCID: PMC7035958 DOI: 10.1016/j.ejpn.2020.01.006] [Citation(s) in RCA: 23] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 05/31/2019] [Revised: 01/03/2020] [Accepted: 01/04/2020] [Indexed: 12/19/2022]
Abstract
Our understanding of the genetic aetiology of paediatric epilepsies has grown substantially over the last decade. However, in order to translate improved diagnostics to personalised treatments, there is an urgent need to link molecular pathophysiology in epilepsy to whole-brain dynamics in seizures. Zebrafish have emerged as a promising new animal model for epileptic seizure disorders, with particular relevance for genetic and developmental epilepsies. As a novel model organism for epilepsy research they combine key advantages: the small size of larval zebrafish allows high throughput in vivo experiments; the availability of advanced genetic tools allows targeted modification to model specific human genetic disorders (including genetic epilepsies) in a vertebrate system; and optical access to the entire central nervous system has provided the basis for advanced microscopy technologies to image structure and function in the intact larval zebrafish brain. There is a growing body of literature describing and characterising features of epileptic seizures and epilepsy in larval zebrafish. Recently genetically encoded calcium indicators have been used to investigate the neurobiological basis of these seizures with light microscopy. This approach offers a unique window into the multiscale dynamics of epileptic seizures, capturing both whole-brain dynamics and single-cell behaviour concurrently. At the same time, linking observations made using calcium imaging in the larval zebrafish brain back to an understanding of epileptic seizures largely derived from cortical electrophysiological recordings in human patients and mammalian animal models is non-trivial. In this review we briefly illustrate the state of the art of epilepsy research in zebrafish with particular focus on calcium imaging of epileptic seizures in the larval zebrafish. We illustrate the utility of a dynamic systems perspective on the epileptic brain for providing a principled approach to linking observations across species and identifying those features of brain dynamics that are most relevant to epilepsy. In the following section we survey the literature for imaging features associated with epilepsy and epileptic seizures and link these to observations made from humans and other more traditional animal models. We conclude by identifying the key challenges still facing epilepsy research in the larval zebrafish and indicate strategies for future research to address these and integrate more directly with the themes and questions that emerge from investigating epilepsy in other model systems and human patients.
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Affiliation(s)
- D R W Burrows
- MRC Centre for Neurodevelopmental Disorders, Institute of Psychiatry, Psychology and Neuroscience, King's College London, London, UK
| | - É Samarut
- Department of Neurosciences, Research Center of the University of Montreal Hospital Center, Montreal, Quebec, Canada
| | - J Liu
- Department of Neurological Surgery and Weill Institute for Neuroscience, University of California, San Francisco, San Francisco, CA, USA
| | - S C Baraban
- Department of Neurological Surgery and Weill Institute for Neuroscience, University of California, San Francisco, San Francisco, CA, USA
| | - M P Richardson
- Department of Basic and Clinical Neuroscience, Institute of Psychiatry, Psychology and Neuroscience, King's College London, London, UK
| | - M P Meyer
- MRC Centre for Neurodevelopmental Disorders, Institute of Psychiatry, Psychology and Neuroscience, King's College London, London, UK; Centre for Developmental Neurobiology, Institute of Psychiatry, Psychology and Neuroscience, King's College London, London, UK
| | - R E Rosch
- MRC Centre for Neurodevelopmental Disorders, Institute of Psychiatry, Psychology and Neuroscience, King's College London, London, UK; Department of Bioengineering, University of Pennsylvania, Philadelphia, PA, USA; Department of Paediatric Neurology, Great Ormond Street Hospital for Children NHS Foundation Trust, London, UK.
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100
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Kantner M, Koprucki T. Beyond just "flattening the curve": Optimal control of epidemics with purely non-pharmaceutical interventions. J Math Ind 2020; 10:23. [PMID: 32834921 PMCID: PMC7432561 DOI: 10.1186/s13362-020-00091-3] [Citation(s) in RCA: 25] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/23/2020] [Accepted: 08/06/2020] [Indexed: 05/20/2023]
Abstract
When effective medical treatment and vaccination are not available, non-pharmaceutical interventions such as social distancing, home quarantine and far-reaching shutdown of public life are the only available strategies to prevent the spread of epidemics. Based on an extended SEIR (susceptible-exposed-infectious-recovered) model and continuous-time optimal control theory, we compute the optimal non-pharmaceutical intervention strategy for the case that a vaccine is never found and complete containment (eradication of the epidemic) is impossible. In this case, the optimal control must meet competing requirements: First, the minimization of disease-related deaths, and, second, the establishment of a sufficient degree of natural immunity at the end of the measures, in order to exclude a second wave. Moreover, the socio-economic costs of the intervention shall be kept at a minimum. The numerically computed optimal control strategy is a single-intervention scenario that goes beyond heuristically motivated interventions and simple "flattening of the curve". Careful analysis of the computed control strategy reveals, however, that the obtained solution is in fact a tightrope walk close to the stability boundary of the system, where socio-economic costs and the risk of a new outbreak must be constantly balanced against one another. The model system is calibrated to reproduce the initial exponential growth phase of the COVID-19 pandemic in Germany.
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Affiliation(s)
- Markus Kantner
- Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Mohrenstr. 39, Berlin, 10117 Germany
| | - Thomas Koprucki
- Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Mohrenstr. 39, Berlin, 10117 Germany
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