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Fumagalli I, Pagani S, Vergara C, Dede’ L, Adebo DA, Del Greco M, Frontera A, Luciani GB, Pontone G, Scrofani R, Quarteroni A. The role of computational methods in cardiovascular medicine: a narrative review. Transl Pediatr 2024; 13:146-163. [PMID: 38323181 PMCID: PMC10839285 DOI: 10.21037/tp-23-184] [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] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 03/20/2023] [Accepted: 12/13/2023] [Indexed: 02/08/2024] Open
Abstract
Background and Objective Computational models of the cardiovascular system allow for a detailed and quantitative investigation of both physiological and pathological conditions, thanks to their ability to combine clinical-possibly patient-specific-data with physical knowledge of the processes underlying the heart function. These models have been increasingly employed in clinical practice to understand pathological mechanisms and their progression, design medical devices, support clinicians in improving therapies. Hinging upon a long-year experience in cardiovascular modeling, we have recently constructed a computational multi-physics and multi-scale integrated model of the heart for the investigation of its physiological function, the analysis of pathological conditions, and to support clinicians in both diagnosis and treatment planning. This narrative review aims to systematically discuss the role that such model had in addressing specific clinical questions, and how further impact of computational models on clinical practice are envisaged. Methods We developed computational models of the physical processes encompassed by the heart function (electrophysiology, electrical activation, force generation, mechanics, blood flow dynamics, valve dynamics, myocardial perfusion) and of their inherently strong coupling. To solve the equations of such models, we devised advanced numerical methods, implemented in a flexible and highly efficient software library. We also developed computational procedures for clinical data post-processing-like the reconstruction of the heart geometry and motion from diagnostic images-and for their integration into computational models. Key Content and Findings Our integrated computational model of the heart function provides non-invasive measures of indicators characterizing the heart function and dysfunctions, and sheds light on its underlying processes and their coupling. Moreover, thanks to the close collaboration with several clinical partners, we addressed specific clinical questions on pathological conditions, such as arrhythmias, ventricular dyssynchrony, hypertrophic cardiomyopathy, degeneration of prosthetic valves, and the way coronavirus disease 2019 (COVID-19) infection may affect the cardiac function. In multiple cases, we were also able to provide quantitative indications for treatment. Conclusions Computational models provide a quantitative and detailed tool to support clinicians in patient care, which can enhance the assessment of cardiac diseases, the prediction of the development of pathological conditions, and the planning of treatments and follow-up tests.
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Affiliation(s)
- Ivan Fumagalli
- MOX Laboratory, Department of Mathematics, Politecnico di Milano, Milan, Italy
| | - Stefano Pagani
- MOX Laboratory, Department of Mathematics, Politecnico di Milano, Milan, Italy
| | - Christian Vergara
- Laboratory of Biological Structures Mechanics (LaBS), Department of Chemistry, Materials and Chemical Engineering “Giulio Natta”, Politecnico di Milano, Milan, Italy
| | - Luca Dede’
- MOX Laboratory, Department of Mathematics, Politecnico di Milano, Milan, Italy
| | - Dilachew A. Adebo
- Children’s Heart Institute, Hermann Children’s Hospital, University of Texas Health Science Center, McGovern Medical School, Houston, TX, USA
| | - Maurizio Del Greco
- Department of Cardiology, S. Maria del Carmine Hospital, Rovereto, Italy
| | - Antonio Frontera
- Electrophysiology Department, De Gasperis Cardio Center, ASST Great Metropolitan Hospital Niguarda, Milan, Italy
| | | | - Gianluca Pontone
- Department of Perioperative Cardiology and Cardiovascular Imaging, Centro Cardiologico Monzino IRCSS, Milan, Italy
- Department of Biomedical, Surgical and Dental Sciences, University of Milan, Milan, Italy
| | - Roberto Scrofani
- Cardiovascular Department, Fondazione IRCCS Ca’ Granda Ospedale Maggiore Policlinico, Milan, Italy
| | - Alfio Quarteroni
- MOX Laboratory, Department of Mathematics, Politecnico di Milano, Milan, Italy
- Institute of Mathematics, École Polytechnique Fédérale de Lausanne, Switzerland
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Emon B, Joy MSH, Lalonde L, Ghrayeb A, Doha U, Ladehoff L, Brockstein R, Saengow C, Ewoldt RH, Saif MTA. Nuclear deformation regulates YAP dynamics in cancer associated fibroblasts. Acta Biomater 2024; 173:93-108. [PMID: 37977292 PMCID: PMC10848212 DOI: 10.1016/j.actbio.2023.11.015] [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: 07/20/2023] [Revised: 11/04/2023] [Accepted: 11/09/2023] [Indexed: 11/19/2023]
Abstract
Cells cultured on stiff 2D substrates exert high intracellular force, resulting in mechanical deformation of their nuclei. This nuclear deformation (ND) plays a crucial role in the transport of Yes Associated Protein (YAP) from the cytoplasm to the nucleus. However, cells in vivo are in soft 3D environment with potentially much lower intracellular forces. Whether and how cells may deform their nuclei in 3D for YAP localization remains unclear. Here, by culturing human colon cancer associated fibroblasts (CAFs) on 2D, 2.5D, and 3D substrates, we differentiated the effects of stiffness, force, and ND on YAP localization. We found that nuclear translocation of YAP depends on the degree of ND irrespective of dimensionality, stiffness and total force. ND induced by the perinuclear force, not the total force, and nuclear membrane curvature correlate strongly with YAP activation. Immunostained slices of human tumors further supported the association between ND and YAP nuclear localization, suggesting ND as a potential biomarker for YAP activation in tumors. Additionally, we conducted quantitative analysis of the force dynamics of CAFs on 2D substrates to construct a stochastic model of YAP kinetics. This model revealed that the probability of YAP nuclear translocation, as well as the residence time in the nucleus follow a power law. This study provides valuable insights into the regulatory mechanisms governing YAP dynamics and highlights the significance of threshold activation in YAP localization. STATEMENT OF SIGNIFICANCE: Yes Associated Protein (YAP), a transcription cofactor, has been identified as one of the drivers of cancer progression. High tumor stiffness is attributed to driving YAP to the nucleus, wherein it activates pro-metastatic genes. Here we show, using cancer associated fibroblasts, that YAP translocation to the nucleus depends on the degree of nuclear deformation, irrespective of stiffness. We also identified that perinuclear force induced membrane curvature correlates strongly with YAP nuclear transport. A novel stochastic model of YAP kinetics unveiled a power law relationship between the activation threshold and persistence time of YAP in the nucleus. Overall, this study provides novel insights into the regulatory mechanisms governing YAP dynamics and the probability of activation that is of immense clinical significance.
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Affiliation(s)
| | | | | | | | | | | | | | - Chaimongkol Saengow
- Mechanical Science & Engineering; Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign
| | - Randy H Ewoldt
- Mechanical Science & Engineering; Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign
| | - M Taher A Saif
- Mechanical Science & Engineering; Bioengineering; Cancer Center at Illinois.
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Africa PC, Piersanti R, Regazzoni F, Bucelli M, Salvador M, Fedele M, Pagani S, Dede' L, Quarteroni A. lifex-ep: a robust and efficient software for cardiac electrophysiology simulations. BMC Bioinformatics 2023; 24:389. [PMID: 37828428 PMCID: PMC10571323 DOI: 10.1186/s12859-023-05513-8] [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: 08/03/2023] [Accepted: 10/02/2023] [Indexed: 10/14/2023] Open
Abstract
BACKGROUND Simulating the cardiac function requires the numerical solution of multi-physics and multi-scale mathematical models. This underscores the need for streamlined, accurate, and high-performance computational tools. Despite the dedicated endeavors of various research teams, comprehensive and user-friendly software programs for cardiac simulations, capable of accurately replicating both normal and pathological conditions, are still in the process of achieving full maturity within the scientific community. RESULTS This work introduces [Formula: see text]-ep, a publicly available software for numerical simulations of the electrophysiology activity of the cardiac muscle, under both normal and pathological conditions. [Formula: see text]-ep employs the monodomain equation to model the heart's electrical activity. It incorporates both phenomenological and second-generation ionic models. These models are discretized using the Finite Element method on tetrahedral or hexahedral meshes. Additionally, [Formula: see text]-ep integrates the generation of myocardial fibers based on Laplace-Dirichlet Rule-Based Methods, previously released in Africa et al., 2023, within [Formula: see text]-fiber. As an alternative, users can also choose to import myofibers from a file. This paper provides a concise overview of the mathematical models and numerical methods underlying [Formula: see text]-ep, along with comprehensive implementation details and instructions for users. [Formula: see text]-ep features exceptional parallel speedup, scaling efficiently when using up to thousands of cores, and its implementation has been verified against an established benchmark problem for computational electrophysiology. We showcase the key features of [Formula: see text]-ep through various idealized and realistic simulations conducted in both normal and pathological scenarios. Furthermore, the software offers a user-friendly and flexible interface, simplifying the setup of simulations using self-documenting parameter files. CONCLUSIONS [Formula: see text]-ep provides easy access to cardiac electrophysiology simulations for a wide user community. It offers a computational tool that integrates models and accurate methods for simulating cardiac electrophysiology within a high-performance framework, while maintaining a user-friendly interface. [Formula: see text]-ep represents a valuable tool for conducting in silico patient-specific simulations.
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Affiliation(s)
- Pasquale Claudio Africa
- MOX, Department of Mathematics, Politecnico di Milano, Milano, Italy
- mathLab, Mathematics Area, SISSA International School for Advanced Studies, Trieste, Italy
| | - Roberto Piersanti
- MOX, Department of Mathematics, Politecnico di Milano, Milano, Italy.
| | | | - Michele Bucelli
- MOX, Department of Mathematics, Politecnico di Milano, Milano, Italy
| | - Matteo Salvador
- MOX, Department of Mathematics, Politecnico di Milano, Milano, Italy
- Institute for Computational and Mathematical Engineering, Stanford University, Stanford, California, USA
| | - Marco Fedele
- MOX, Department of Mathematics, Politecnico di Milano, Milano, Italy
| | - Stefano Pagani
- MOX, Department of Mathematics, Politecnico di Milano, Milano, Italy
| | - Luca Dede'
- MOX, Department of Mathematics, Politecnico di Milano, Milano, Italy
| | - Alfio Quarteroni
- MOX, Department of Mathematics, Politecnico di Milano, Milano, Italy
- Institute of Mathematics, École Polytechnique Fédérale de Lausanne, Lausanne, Professor emeritus, Switzerland
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Shakya K, Ahirwar D, Nabeel PM, Roy Chowdhury S. Carotid hemodynamic response to external pressure and comparison with induced-stenosis progression: a fluid-structure interaction study. Comput Methods Biomech Biomed Engin 2023; 26:1595-1609. [PMID: 36200483 DOI: 10.1080/10255842.2022.2128785] [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] [Received: 07/19/2022] [Revised: 09/02/2022] [Accepted: 09/11/2022] [Indexed: 11/03/2022]
Abstract
Non-invasive stenosis detection has always been difficult. A new concept of applying external pressure over the artery was compared with stenosis growth in this computational study. When stenosis develops, the artery constricts, obstructing blood flow in that area. Under external pressure, the constricted artery behaves similarly. The current fluid-structure interaction study compares the hemodynamic parameters of a stenosed artery and an artery subjected to external pressure. Significant similarities were discovered when the velocity profile and arterial displacement for both scenarios were compared. This study can be used to characterise stenosis experimentally while remaining non-invasive.
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Affiliation(s)
- Kshitij Shakya
- School of Computing and Electrical Engineering, Indian Institute of Technology Mandi, Mandi, Himachal Pradesh, India
| | - Dalchand Ahirwar
- School of Computing and Electrical Engineering, Indian Institute of Technology Mandi, Mandi, Himachal Pradesh, India
| | - P M Nabeel
- Healthcare Technology Innovation Centre, Indian Institute of Technology Madras, Chennai, Tamil Nadu, India
| | - Shubhajit Roy Chowdhury
- School of Computing and Electrical Engineering, Indian Institute of Technology Mandi, Mandi, Himachal Pradesh, India
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Mazhar F, Bartolucci C, Regazzoni F, Paci M, Dedè L, Quarteroni A, Corsi C, Severi S. A detailed mathematical model of the human atrial cardiomyocyte: integration of electrophysiology and cardiomechanics. J Physiol 2023. [PMID: 37641426 DOI: 10.1113/jp283974] [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] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2022] [Accepted: 08/02/2023] [Indexed: 08/31/2023] Open
Abstract
Mechano-electric regulations (MER) play an important role in the maintenance of cardiac performance. Mechano-calcium and mechano-electric feedback (MCF and MEF) pathways adjust the cardiomyocyte contractile force according to mechanical perturbations and affects electro-mechanical coupling. MER integrates all these regulations in one unit resulting in a complex phenomenon. Computational modelling is a useful tool to accelerate the mechanistic understanding of complex experimental phenomena. We have developed a novel model that integrates the MER loop for human atrial cardiomyocytes with proper consideration of feedforward and feedback pathways. The model couples a modified version of the action potential (AP) Koivumäki model with the contraction model by Quarteroni group. The model simulates iso-sarcometric and isometric twitches and the feedback effects on AP and Ca2+ -handling. The model showed a biphasic response of Ca2+ transient (CaT) peak to increasing pacing rates and highlights the possible mechanisms involved. The model has shown a shift of the threshold for AP and CaT alternans from 4.6 to 4 Hz under post-operative atrial fibrillation, induced by depressed SERCA activity. The alternans incidence was dependent on a chain of mechanisms including RyRs availability time, MCF coupling, CaMKII phosphorylation, and the stretch levels. As a result, the model predicted a 10% slowdown of conduction velocity for a 20% stretch, suggesting a role of stretch in creation of substrate formation for atrial fibrillation. Overall, we conclude that the developed model provides a physiological CaT followed by a physiological twitch. This model can open pathways for the future studies of human atrial electromechanics. KEY POINTS: With the availability of human atrial cellular data, interest in atrial-specific model integration has been enhanced. We have developed a detailed mathematical model of human atrial cardiomyocytes including the mechano-electric regulatory loop. The model has gone through calibration and evaluation phases against a wide collection of available human in-vitro data. The usefulness of the model for analysing clinical problems has been preliminaryly tested by simulating the increased incidence of Ca2+ transient and action potential alternans at high rates in post-operative atrial fibrillation condition. The model determines the possible role of mechano-electric feedback in alternans incidence, which can increase vulnerability to atrial arrhythmias by varying stretch levels. We found that our physiologically accurate description of Ca2+ handling can reproduce many experimental phenomena and can help to gain insights into the underlying pathophysiological mechanisms.
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Affiliation(s)
- Fazeelat Mazhar
- Department of Electrical, Electronic and Information Engineering 'Guglielmo Marconi', University of Bologna, Cesena, Italy
| | - Chiara Bartolucci
- Department of Electrical, Electronic and Information Engineering 'Guglielmo Marconi', University of Bologna, Cesena, Italy
| | | | - Michelangelo Paci
- Department of Electrical, Electronic and Information Engineering 'Guglielmo Marconi', University of Bologna, Cesena, Italy
- BioMediTech, Faculty of Medicine and Health Technology, Tampere University, Tampere, Finland
| | - Luca Dedè
- MOX - Dipartimento di Matematica, Politecnico di Milano, Milan, Italy
| | - Alfio Quarteroni
- MOX - Dipartimento di Matematica, Politecnico di Milano, Milan, Italy
- Mathematics Institute, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
| | - Cristiana Corsi
- Department of Electrical, Electronic and Information Engineering 'Guglielmo Marconi', University of Bologna, Cesena, Italy
| | - Stefano Severi
- Department of Electrical, Electronic and Information Engineering 'Guglielmo Marconi', University of Bologna, Cesena, Italy
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Jeknić S, Kudo T, Song JJ, Covert MW. An optimized reporter of the transcription factor hypoxia-inducible factor 1α reveals complex HIF-1α activation dynamics in single cells. J Biol Chem 2023; 299:104599. [PMID: 36907438 PMCID: PMC10124923 DOI: 10.1016/j.jbc.2023.104599] [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: 10/18/2022] [Revised: 02/08/2023] [Accepted: 02/20/2023] [Indexed: 03/13/2023] Open
Abstract
Immune cells adopt a variety of metabolic states to support their many biological functions, which include fighting pathogens, removing tissue debris, and tissue remodeling. One of the key mediators of these metabolic changes is the transcription factor hypoxia-inducible factor 1α (HIF-1α). Single-cell dynamics have been shown to be an important determinant of cell behavior; however, despite the importance of HIF-1α, little is known about its single-cell dynamics or their effect on metabolism. To address this knowledge gap, here we optimized a HIF-1α fluorescent reporter and applied it to study single-cell dynamics. First, we showed that single cells are likely able to differentiate multiple levels of prolyl hydroxylase inhibition, a marker of metabolic change, via HIF-1α activity. We then applied a physiological stimulus known to trigger metabolic change, interferon-γ, and observed heterogeneous, oscillatory HIF-1α responses in single cells. Finally, we input these dynamics into a mathematical model of HIF-1α-regulated metabolism and discovered a profound difference between cells exhibiting high versus low HIF-1α activation. Specifically, we found cells with high HIF-1α activation are able to meaningfully reduce flux through the tricarboxylic acid cycle and show a notable increase in the NAD+/NADH ratio compared with cells displaying low HIF-1α activation. Altogether, this work demonstrates an optimized reporter for studying HIF-1α in single cells and reveals previously unknown principles of HIF-1α activation.
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Affiliation(s)
- Stevan Jeknić
- Department of Bioengineering, Stanford University, Stanford, California, USA
| | - Takamasa Kudo
- Department of Chemical and Systems Biology, Stanford University, Stanford, California, USA
| | - Joanna J Song
- Department of Bioengineering, Stanford University, Stanford, California, USA
| | - Markus W Covert
- Department of Bioengineering, Stanford University, Stanford, California, USA.
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7
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Thoma E. Thermodynamic and scaling limits of the non-Gaussian membrane model. ANN PROBAB 2023. [DOI: 10.1214/22-aop1609] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/12/2023]
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8
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Katayama S, Murooka M, Tazaki Y. Model predictive control of legged and humanoid robots: models and algorithms. Adv Robot 2023. [DOI: 10.1080/01691864.2023.2168134] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/11/2023]
Affiliation(s)
- Sotaro Katayama
- Graduate School of Informatics, Kyoto University, Kyoto, Japan
| | | | - Yuichi Tazaki
- Graduate School of Engineering, Kobe University, Kobe, Japan
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Lai KK, Mishra SK, Singh V. Ostrowski Type Inequalities via Some Exponentially s-Preinvex Functions on Time Scales with Applications. Symmetry (Basel) 2023; 15:410. [DOI: 10.3390/sym15020410] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/09/2023] Open
Abstract
Integral inequalities concerned with convexity have many applications in several fields of mathematics in which symmetry plays an important role. In the theory of convexity, there exist strong connections between convexity and symmetry. If we are working on one of the concepts, then it can be applied to the other of them. In this paper, we establish some novel generalizations of Ostrowski type inequalities for exponentially s-preinvex and s-preinvex functions on time scale by using Hölder inequality and Montgomery Identity. We also obtain applications to some special means. These results are motivated by the symmetric results obtained in the recent article by Abbasi and Anwar in 2022 on Ostrowski type inequalities for exponentially s-convex functions and s-convex functions on time scale. Moreover, we discuss several special cases of the results obtained in this paper.
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10
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Thuy LTH, Phuong CX. Deconvolution problem of cumulative distribution function with heteroscedastic errors. J Korean Stat Soc 2023. [DOI: 10.1007/s42952-023-00203-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/22/2023]
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11
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Zhang X, Wang Y, Zhu L, Chen H, Li H, Wu L. Robust variable structure discovery based on tilted empirical risk minimization. APPL INTELL 2023. [DOI: 10.1007/s10489-022-04409-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023]
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12
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Celora GL, Byrne HM, Kevrekidis PG. Spatio-temporal modelling of phenotypic heterogeneity in tumour tissues and its impact on radiotherapy treatment. J Theor Biol 2023; 556:111248. [PMID: 36150537 DOI: 10.1016/j.jtbi.2022.111248] [Citation(s) in RCA: 1] [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: 12/20/2021] [Revised: 08/02/2022] [Accepted: 08/17/2022] [Indexed: 11/20/2022]
Abstract
We present a mathematical model that describes how tumour heterogeneity evolves in a tissue slice that is oxygenated by a single blood vessel. Phenotype is identified with the stemness level of a cell and determines its proliferative capacity, apoptosis propensity and response to treatment. Our study is based on numerical bifurcation analysis and dynamical simulations of a system of coupled, non-local (in phenotypic "space") partial differential equations that link the phenotypic evolution of the tumour cells to local tissue oxygen levels. In our formulation, we consider a 1D geometry where oxygen is supplied by a blood vessel located on the domain boundary and consumed by the tumour cells as it diffuses through the tissue. For biologically relevant parameter values, the system exhibits multiple steady states; in particular, depending on the initial conditions, the tumour is either eliminated ("tumour-extinction") or it persists ("tumour-invasion"). We conclude by using the model to investigate tumour responses to radiotherapy, and focus on identifying radiotherapy strategies which can eliminate the tumour. Numerical simulations reveal how phenotypic heterogeneity evolves during treatment and highlight the critical role of tissue oxygen levels on the efficacy of radiation protocols that are commonly used in the clinic.
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Ferrante P, Preziosi L, Scianna M. Modeling hypoxia-related inflammation scenarios. Math Biosci 2023; 355:108952. [PMID: 36528132 DOI: 10.1016/j.mbs.2022.108952] [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] [Received: 05/15/2022] [Revised: 11/26/2022] [Accepted: 12/01/2022] [Indexed: 12/15/2022]
Abstract
Cells respond to hypoxia via the activation of three isoforms of Hypoxia Inducible Factors (HIFs), that are characterized by different activation times. HIF overexpression has many effects on cell behavior, such as change in metabolism, promotion of angiogenic processes and elicitation of a pro-inflammatory response. These effects are driving forces of malignant progression in cancer cells. In this work we study in detail hypoxia-induced dynamics of HIF1α and HIF2α, which are the most studied isoforms, comparing available experimental data on their evolution in tumor cells with the results obtained integrating the deduced mathematical model. Then, we examine the possible scenarios that characterize the link between hypoxia and inflammation via the activation of NFkB (Nuclear Factor k-light-chain-enhancer of activated B cells) when the dimensionless groups of parameters of the mathematical model change. In this way we are able to discuss why and when hypoxic conditions lead to acute or chronic inflammatory states.
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Affiliation(s)
- P Ferrante
- Department Mathematical Sciences, Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino, Italy; Candiolo Cancer Institute FPO-IRCCS, Candiolo, Italy.
| | - L Preziosi
- Department Mathematical Sciences, Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino, Italy.
| | - M Scianna
- Department Mathematical Sciences, Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino, Italy.
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Li Y, Xu Z. A bibliometric analysis and basic model introduction of opinion dynamics. APPL INTELL 2022. [DOI: 10.1007/s10489-022-04368-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
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Duangpan A, Boonklurb R, Rakwongwan U, Sutthimat P. Analytical Formulas Using Affine Transformation for Pricing Generalized Swaps in Commodity Markets with Stochastic Convenience Yields. Symmetry (Basel) 2022; 14:2385. [DOI: 10.3390/sym14112385] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
This paper presents analytical formulas for pricing generalized swaps, including the moment swap, gamma swap, entropy swap and self-quantoed variance swap. The formulas are based on closed-form formulas for the conditional expectations of the product of the price and its logarithm and the product of the price and the convenience yield obtained by solving a partial differential equation corresponding to the infinitesimal generator for the two-dimensional diffusion process. In this respect, the formulas obtained are combinatorial in nature and are solved via an affine transformation involving the complete Bell polynomials. The formulas are quite suitable for practical usage with symmetric and skew-symmetric properties, i.e., they are simpler and more compact compared with those existing in the literature. Moreover, for moments swaps, we show in general that the strike price does not depend on the initial spot price but depends only on the initial convenience yield, which highlights the resulting versatility in this respect.
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Tranthi J, Botmart T. A novel criteria on exponentially passive analysis for Takagi-Sugeno fuzzy of neutral dynamic system with various time-varying delays. PLoS One 2022; 17:e0275057. [PMID: 36206211 DOI: 10.1371/journal.pone.0275057] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/01/2022] [Accepted: 09/09/2022] [Indexed: 11/19/2022] Open
Abstract
This paper is the first studying on designing exponentially passive analysis for T-S fuzzy of dynamic systems with various time-varying delays such as neutral, discrete, and distributed time-varying delays. Constructing the new Lyapunov-Krasovskii function and the Newton-Leibniz theory, the zero equations, and the matrix inequality techniques, the multiple delay-dependent criteria, with assuring exponentially passive on the discussed T-S fuzzy system, are defined in respect of linear matrix inequalities (LMIs) that can be checked easily using the LMI toolbox of MATLAB. Those approaches give less conservative, exponentially passive criteria for special cases of general stability of a neutral differential system. Furthermore, the results of this study are delay-dependent, which depend on the lower and upper bound with the time-varying delay. Lastly, some numerical examples illustrate the performance of our criteria based on the results obtained and summarize some of the previous achievements.
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Tran KQ, Le BT. On exponential stability of non-autonomous stochastic differential equations with Markovian switching. Stat Probab Lett 2022; 189:109602. [DOI: 10.1016/j.spl.2022.109602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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Lubenia PVN, Mendoza ER, Lao AR. Reaction Network Analysis of Metabolic Insulin Signaling. Bull Math Biol 2022; 84:129. [PMID: 36168001 DOI: 10.1007/s11538-022-01087-3] [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: 04/09/2022] [Accepted: 09/15/2022] [Indexed: 11/02/2022]
Abstract
Absolute concentration robustness (ACR) and concordance are novel concepts in the theory of robustness and stability within Chemical Reaction Network Theory. In this paper, we have extended Shinar and Feinberg's reaction network analysis approach to the insulin signaling system based on recent advances in decomposing reaction networks. We have shown that the network with 20 species, 35 complexes, and 35 reactions is concordant, implying at most one positive equilibrium in each of its stoichiometric compatibility class. We have obtained the system's finest independent decomposition consisting of 10 subnetworks, a coarsening of which reveals three subnetworks which are not only functionally but also structurally important. Utilizing the network's deficiency-oriented coarsening, we have developed a method to determine positive equilibria for the entire network. Our analysis has also shown that the system has ACR in 8 species all coming from a deficiency zero subnetwork. Interestingly, we have shown that, for a set of rate constants, the insulin-regulated glucose transporter GLUT4 (important in glucose energy metabolism), has stable ACR.
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Affiliation(s)
- Patrick Vincent N Lubenia
- Systems and Computational Biology Research Unit, Center for Natural Sciences and Environmental Research, 2401 Taft Avenue, Manila, 0922, Metro Manila, Philippines
| | - Eduardo R Mendoza
- Systems and Computational Biology Research Unit, Center for Natural Sciences and Environmental Research, 2401 Taft Avenue, Manila, 0922, Metro Manila, Philippines.,Department of Mathematics and Statistics, De La Salle University, 2401 Taft Avenue, Manila, 0922, Metro Manila, Philippines.,Max Planck Institute of Biochemistry, Am Klopferspitz 18, 82152, Martinsried, Munich, Germany
| | - Angelyn R Lao
- Systems and Computational Biology Research Unit, Center for Natural Sciences and Environmental Research, 2401 Taft Avenue, Manila, 0922, Metro Manila, Philippines. .,Department of Mathematics and Statistics, De La Salle University, 2401 Taft Avenue, Manila, 0922, Metro Manila, Philippines. .,Center for Complexity and Emerging Technologies, 2401 Taft Avenue, Manila, 0922, Metro Manila, Philippines.
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Bezemek Z, Spiliopoulos K. Large deviations for interacting multiscale particle systems. Stoch Process Their Appl 2022. [DOI: 10.1016/j.spa.2022.09.010] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 10/14/2022]
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Rossini L, Bono Rosselló N, Contarini M, Speranza S, Garone E. Modelling ectotherms’ populations considering physiological age structure and spatial motion: A novel approach. ECOL INFORM 2022. [DOI: 10.1016/j.ecoinf.2022.101703] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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López-alfonso S, López-pellicer M, Moll-lópez S, Sánchez-ruiz LM. A Survey on Valdivia Open Question on Nikodým Sets. Mathematics 2022; 10:2660. [DOI: 10.3390/math10152660] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Let A be an algebra of subsets of a set Ω and ba(A) the Banach space of bounded finitely additive scalar-valued measures on A endowed with the variation norm. A subset B of A is a Nikodým set for ba(A) if each countable B-pointwise bounded subset M of ba(A) is norm bounded. A subset B of A is a Grothendieck set for ba(A) if for each bounded sequence μnn=1∞ in ba(A) the B-pointwise convergence on ba(A) implies its ba(A)*-pointwise convergence on ba(A). A subset B of an algebra A is a strong-Nikodým (Grothendieck) set for ba(A) if in each increasing covering {Bn:n∈N} of B there exists Bm which is a Nikodým (Grothendieck) set for ba(A). The answer of the following open question for an algebra A of subsets of a set Ω, proposed by Valdivia in 2013, has not yet been found: Is it true that if A is a Nikodým set for ba(A) then A is a strong Nikodým set for ba(A)? In this paper we surveyed some results related to this Valdivia’s open question, as well as the corresponding problem for strong Grothendieck sets. The new Propositions 1 and 3 provide more simplified proofs, particularly in their application to Theorems 1 and 2, which were the main results surveyed. Moreover, the proofs of almost all other propositions are wholly or partially original.
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Alshehry AS, Habeb JM, Abu-dawwas R, Alrawabdeh A. Graded Weakly 2-Absorbing Ideals over Non-Commutative Graded Rings. Symmetry (Basel) 2022; 14:1472. [DOI: 10.3390/sym14071472] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
Let G be a group and R be a G-graded ring. In this paper, we present and examine the concept of graded weakly 2-absorbing ideals as in generality of graded weakly prime ideals in a graded ring which is not commutative, and demonstrates that the symmetry is obtained as a lot of the outcomes in commutative graded rings remain in graded rings that are not commutative.
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Badea L. On the Convergence of the Damped Additive Schwarz Methods and the Subdomain Coloring. MCA 2022; 27:59. [DOI: 10.3390/mca27040059] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
Abstract
In this paper, we consider that the subdomains of the domain decomposition are colored such that the subdomains with the same color do not intersect and introduce and analyze the convergence of a damped additive Schwarz method related to such a subdomain coloring for the resolution of variational inequalities and equations. In this damped method, a single damping value is associated with all the subdomains having the same color. We first make this analysis both for variational inequalities and, as a special case, for equations in an abstract framework. By introducing an assumption on the decomposition of the convex set of the variational inequality, we theoretically analyze in a reflexive Banach space the convergence of the damped additive Schwarz method. The introduced assumption contains a constant C0, and we explicitly write the expression of the convergence rates, depending on the number of colors and the constant C0, and find the values of the damping constants which minimize them. For problems in the finite element spaces, we write the constant C0 as a function of the overlap parameter of the domain decomposition and the number of colors of the subdomains. We show that, for a fixed overlap parameter, the convergence rate, as a function of the number of subdomains has an upper limit which depends only on the number of the colors of the subdomains. Obviously, this limit is independent of the total number of subdomains. Numerical results are in agreement with the theoretical ones. They have been performed for an elasto-plastic problem to verify the theoretical predictions concerning the choice of the damping parameter, the dependence of the convergence on the overlap parameter and on the number of subdomains.
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Van Hieu D, Cho YJ, Quy PK, Ha NH. An effective iterative projection method for variational inequalities in Hilbert spaces. Soft comput 2022. [DOI: 10.1007/s00500-022-07319-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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González-parra G, Chen-charpentier B, Arenas AJ, Díaz-rodríguez M. Mathematical Modeling of Physical Capital Diffusion Using a Spatial Solow Model: Application to Smuggling in Venezuela. Economies 2022; 10:164. [DOI: 10.3390/economies10070164] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Abstract
This study proposes a mathematical modeling approach for the physical capital diffusion through the borders of countries. Physical capital is considered a crucial variable for the economic growth of a nation. Here, we use an extension of the economic Solow model to describe how smuggling affects the economic growth of countries. In particular, we focus on the situation in Venezuela from 2012 to 2015. In this regard, we rely on a nonconcave production function instead of the classical Cobb–Douglas production function. Moreover, we investigate the effect of different physical capital fluxes on economic growth. The physical capital diffusion through the borders of a country is modeled based on a parabolic partial differential equation describing the dynamics of physical capital and boundary conditions of the Neumann type. Smuggling is present at numerous borders between countries and may include fuel, machinery, and food. This smuggling through the borders places challenges on a particular country’s economy. The smuggling problem usually is related to a non-official exchange rate different from the official rate or subsidies. We study the effect of smuggling on the physical capital of a country using an extended Solow model. Numerical simulations are obtained using an explicit finite difference scheme describing how the physical capital diffusion through the border of a country affects its economic growth. The study of physical capital is a paramount aspect of the economic growth of several countries. The results show that when boundary conditions of Neumann type are different from zero, the dynamics of the physical capital differ from the classical economic behavior observed in the classical spatial Solow model without physical capital flux through the borders of countries. In particular, the numerical results show that the physical capital of a country decreases faster as the flux increases on the boundaries. Thus, we can conclude that avoiding smuggling through the frontiers is a crucial factor affecting economic growth.
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Suantai S, Kankam K, Cholamjiak W, Yajai W. Parallel Hybrid Algorithms for a Finite Family of G-Nonexpansive Mappings and Its Application in a Novel Signal Recovery. Mathematics 2022; 10:2140. [DOI: 10.3390/math10122140] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
This article considers a parallel monotone hybrid algorithm for a finite family of G-nonexpansive mapping in Hilbert spaces endowed with graphs and suggests iterative schemes for finding a common fixed point by the two different hybrid projection methods. Moreover, we show the computational performance of our algorithm in comparison to some methods. Strong convergence theorems are proved under suitable conditions. Finally, we give some numerical experiments of our algorithms to show the efficiency and implementation of the LASSO problems in signal recovery with different types of blurred matrices and noise.
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Mihiţ CL, Moţ G, Petruşel G. Ćirić-Type Operators and Common Fixed Point Theorems. Mathematics 2022; 10:1947. [DOI: 10.3390/math10111947] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/10/2022]
Abstract
In the context of a complete metric space, we will consider the common fixed point problem for two self operators. The operators are assumed to satisfy a general contraction type condition inspired by the Ćirić fixed point theorems. Under some appropriate conditions we establish existence, uniqueness and approximation results for the common fixed point. In the same framework, the second problem is to study various stability properties. More precisely, we will obtain sufficient conditions assuring that the common fixed point problem is well-posed and has the Ulam–Hyers stability, as well as the Ostrowski property for the considered problem. Some examples and applications are finally given in order to illustrate the abstract theorems proposed in the first part of the paper. Our results extend and complement some theorems in the recent literature.
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Schultz ES, Olofsson S, Mhamdi A, Mitsos A. Satisfaction of path chance constraints in dynamic optimization problems. Comput Chem Eng 2022. [DOI: 10.1016/j.compchemeng.2022.107899] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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29
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Loy N, Raviola M, Tosin A. Opinion polarization in social networks. Philos Trans A Math Phys Eng Sci 2022; 380:20210158. [PMID: 35400191 DOI: 10.1098/rsta.2021.0158] [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] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/05/2021] [Accepted: 11/07/2021] [Indexed: 06/14/2023]
Abstract
In this paper, we propose a Boltzmann-type kinetic description of opinion formation on social networks, which takes into account a general connectivity distribution of the individuals. We consider opinion exchange processes inspired by the Sznajd model and related simplifications but we do not assume that individuals interact on a regular lattice. Instead, we describe the structure of the social network statistically, assuming that the number of contacts of a given individual determines the probability that their opinion reaches and influences the opinion of another individual. From the kinetic description of the system, we study the evolution of the mean opinion, whence we find precise analytical conditions under which a polarization switch of the opinions, i.e. a change of sign between the initial and the asymptotic mean opinions, occurs. In particular, we show that a non-zero correlation between the initial opinions and the connectivity of the individuals is necessary to observe polarization switch. Finally, we validate our analytical results through Monte Carlo simulations of the stochastic opinion exchange processes on the social network. This article is part of the theme issue 'Kinetic exchange models of societies and economies'.
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Affiliation(s)
- Nadia Loy
- Department of Mathematical Sciences 'G. L. Lagrange', Politecnico di Torino, Torino, Italy
| | - Matteo Raviola
- Department of Mathematical Sciences 'G. L. Lagrange', Politecnico di Torino, Torino, Italy
| | - Andrea Tosin
- Department of Mathematical Sciences 'G. L. Lagrange', Politecnico di Torino, Torino, Italy
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Düring B, Wright O. On a kinetic opinion formation model for pre-election polling. Philos Trans A Math Phys Eng Sci 2022; 380:20210154. [PMID: 35400183 DOI: 10.1098/rsta.2021.0154] [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] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/13/2021] [Accepted: 11/22/2021] [Indexed: 06/14/2023]
Abstract
Motivated by recent successes in model-based pre-election polling, we propose a kinetic model for opinion formation which includes voter demographics and socio-economic factors like age, sex, ethnicity, education level, income and other measurable factors like behaviour in previous elections or referenda as a key driver in the opinion formation dynamics. The model is based on Toscani's kinetic opinion formation model (Toscani G. 2006 Kinetic models of opinion formation. Commun. Math. Sci. 4, 481-496.) and the leader-follower model of Düring et al. (Düring B. et al. 2009 Boltzmann and Fokker-Planck equations modelling opinion formation in the presence of strong leaders. Proc. R. Soc. A 465, 3687-3708.), and leads to a system of coupled Boltzmann-type equations and associated, approximate Fokker-Planck-type systems. Numerical examples using data from general elections in the UK show the effect different demographics have on the opinion formation process and the outcome of elections. This article is part of the theme issue 'Kinetic exchange models of societies and economies'.
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Affiliation(s)
- Bertram Düring
- Mathematics Institute, University of Warwick, Zeeman Building, Coventry CV4 7AL, UK
| | - Oliver Wright
- Mathematics Institute, University of Warwick, Zeeman Building, Coventry CV4 7AL, UK
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Abstract
In this article, we present an extension of the controlled rectangular b-metric spaces, so-called controlled rectangular metric-like spaces, where we keep the symmetry condition and we only change the condition [D(s,r)=0⇔s=r]to[D(s,r)=0⇒s=r], which means we may have a non-zero self distance; also, D(s,s) is not necessarily less than D(s,r). This new type of metric space is a generalization of controlled rectangular b-metric spaces and partial rectangular metric spaces.
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32
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Zhang D, Wang K, Zhang Z, Xu Z, Shao Z, Biegler LT, Tula AK. Generalized Parameter Estimation Method for Model-Based Real‑Time Optimization. Chem Eng Sci 2022. [DOI: 10.1016/j.ces.2022.117754] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Abstract
The main goal of this article is to explore a new type of polynomials, specifically the Gould-Hopper-Laguerre-Sheffer matrix polynomials, through operational techniques. The generating function and operational representations for this new family of polynomials will be established. In addition, these specific matrix polynomials are interpreted in terms of quasi-monomiality. The extended versions of the Gould-Hopper-Laguerre-Sheffer matrix polynomials are introduced, and their characteristics are explored using the integral transform. Further, examples of how these results apply to specific members of the matrix polynomial family are shown.
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34
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Song Y, Chen X. Analysis of Subgradient Extragradient Method for Variational Inequality Problems and Null Point Problems. Symmetry (Basel) 2022; 14:636. [DOI: 10.3390/sym14040636] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
In this paper, we introduce a new numerical method for finding a common solution to variational inequality problems involving monotone mappings and null point problems involving a finite family of inverse-strongly monotone mappings. The method is inspired by the subgradient extragradient method and the regularization method. Strong convergence results of the proposed algorithms have been obtained under some suitable conditions.
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35
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Banerjee M, Kuznetsov M, Udovenko O, Volpert V. Nonlocal Reaction-Diffusion Equations in Biomedical Applications. Acta Biotheor 2022; 70:12. [PMID: 35298702 DOI: 10.1007/s10441-022-09436-4] [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: 10/19/2021] [Accepted: 02/28/2022] [Indexed: 11/01/2022]
Abstract
Nonlocal reaction-diffusion equations describe various biological and biomedical applications. Their mathematical properties are essentially different in comparison with the local equations, and this difference can lead to important biological implications. This review will present the state of the art in the investigation of nonlocal reaction-diffusion models in biomedical applications. We will consider various models arising in mathematical immunology, neuroscience, cancer modelling, and we will discuss their mathematical properties, nonlinear dynamics, resulting spatiotemporal patterns and biological significance.
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36
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Alzabut J, Agarwal RP, Grace SR, Jonnalagadda JM, Selvam AGM, Wang C. A Survey on the Oscillation of Solutions for Fractional Difference Equations. Mathematics 2022; 10:894. [DOI: 10.3390/math10060894] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Abstract
In this paper, we present a systematic study concerning the developments of the oscillation results for the fractional difference equations. Essential preliminaries on discrete fractional calculus are stated prior to giving the main results. Oscillation results are presented in a subsequent order and for different types of equations. The investigation was carried out within the delta and nabla operators.
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37
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Chaturvedi AK, Kumar N. On $$\mathcal {Z}$$-Reversible Rings. Proc Natl Acad Sci , India, Sect A Phys Sci 2022. [DOI: 10.1007/s40010-022-00770-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Abstract
In this paper, we give some remarks on the recent papers on generalized F-contractions. Our results unify and generalize the previous results in the existing literature. Moreover, we give an example to support our results. As an application, we give the existence and uniqueness of a solution to a class of differential equations.
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39
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Zhu L, Zhang Y, Wang B, Zou R, Huang Y, Sun W. Dynamic analysis of equivalent circuit model value of CoP/boron nitride doped carbon for hydrogen evolution reaction. Electrochim Acta 2022; 406:139846. [DOI: 10.1016/j.electacta.2022.139846] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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40
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Moosaei H, Bazikar F, Ketabchi S, Hladík M. Universum parametric-margin ν-support vector machine for classification using the difference of convex functions algorithm. APPL INTELL 2022; 52:2634-54. [DOI: 10.1007/s10489-021-02402-6] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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41
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Italia M, Dercole F, Lucchetti R. Optimal chemotherapy counteracts cancer adaptive resistance in a cell-based, spatially-extended, evolutionary model. Phys Biol 2022; 19. [PMID: 35100568 DOI: 10.1088/1478-3975/ac509c] [Citation(s) in RCA: 4] [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: 11/10/2021] [Accepted: 01/31/2022] [Indexed: 11/12/2022]
Abstract
Most aggressive cancers are incurable due to their fast evolution of drug resistance. We model cancer growth and adaptive response in a simplified cell-based (CB) setting, assuming a genetic resistance to two chemotherapeutic drugs. We show that optimal administration protocols can steer cells resistance and turned it into a weakness for the disease. Our work extends the population-based (PB) model proposed by Orlando et al. (Physical Biology, 2012), in which a homogeneous population of cancer cells evolves according to a fitness landscape. The landscape models three types of trade-offs, differing on whether the cells are more, less, or equal effective when generalizing resistance to two drugs as opposed to specializing to a single one. The CB framework allows us to include genetic heterogeneity, spatial competition, and drugs diffusion, as well as realistic administration protocols. By calibrating our model on Orlando et al.'s assumptions, we show that dynamical protocols that alternate the two drugs minimize the cancer size at the end of (or at mid-points during) treatment. These results significantly differ from those obtained with the homogeneous model---suggesting static protocols under the pro-generalizing and neutral allocation trade-offs---highlighting the important role of spatial and genetic heterogeneities. Our work is the first attempt to search for optimal treatments in a CB setting, a step forward toward realistic clinical applications.
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Affiliation(s)
- Matteo Italia
- Electronics, Information and Bioengineering, Politecnico di Milano, Via Ponzio 34/5, Milano, 20133, ITALY
| | - Fabio Dercole
- Electronics, Information and Bioengineering, Politecnico di Milano, Via Ponzio 34/5, Milano, 20133, ITALY
| | - Roberto Lucchetti
- Mathematics, Politecnico di Milano, Via Edoardo Bonardi, 9, Milano, 20133, ITALY
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Shafqat R, Niazi AUK, Jeelani MB, Alharthi NH. Existence and Uniqueness of Mild Solution Where α∈(1,2) for Fuzzy Fractional Evolution Equations with Uncertainty. Fractal Fract 2022; 6:65. [DOI: 10.3390/fractalfract6020065] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
This paper concerns with the existence and uniqueness of fuzzy fractional evolution equation with uncertainty involves function of form cDαx(t)=f(t,x(t),Dβx(t)),Iαx(0)=x0,x′(0)=x1, where 1<α<2,0<β<1. After determining the equivalent integral form of solution we establish existence and uniqueness by using Rogers conditions, Kooi type conditions and Krasnoselskii-Krein type conditions. In addition, various numerical solutions have been presented to ensure that the main result is true and effective. Finally, a few examples which express fuzzy fractional evolution equations are shown.
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Ge Z. Review of the Latest Progress in Controllability of Stochastic Linear Systems and Stochastic GE-Evolution Operator. Mathematics 2021; 9:3240. [DOI: 10.3390/math9243240] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
According to the spatial dimension, equation type, and time sequence, the latest progress in controllability of stochastic linear systems and some unsolved problems are introduced. Firstly, the exact controllability of stochastic linear systems in finite dimensional spaces is discussed. Secondly, the exact, exact null, approximate, approximate null, and partial approximate controllability of stochastic linear systems in infinite dimensional spaces are considered. Thirdly, the exact, exact null and impulse controllability of stochastic singular linear systems in finite dimensional spaces are investigated. Fourthly, the exact and approximate controllability of stochastic singular linear systems in infinite dimensional spaces are studied. At last, the controllability and observability for a type of time-varying stochastic singular linear systems are studied by using stochastic GE-evolution operator in the sense of mild solution in Banach spaces, some necessary and sufficient conditions are obtained, the dual principle is proved to be true, an example is given to illustrate the validity of the theoretical results obtained in this part, and a problem to be solved is introduced. The main purpose of this paper is to facilitate readers to fully understand the latest research results concerning the controllability of stochastic linear systems and the problems that need to be further studied, and attract more scholars to engage in this research.
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Ahmadova A, Mahmudov NI. Asymptotic Separation of Solutions to Fractional Stochastic Multi-Term Differential Equations. Fractal Fract 2021; 5:256. [DOI: 10.3390/fractalfract5040256] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
In this paper, we study the exact asymptotic separation rate of two distinct solutions of Caputo stochastic multi-term differential equations (Caputo SMTDEs). Our goal in this paper is to establish results of the global existence and uniqueness and continuity dependence of the initial values of the solutions to Caputo SMTDEs with non-permutable matrices of order α∈(12,1) and β∈(0,1) whose coefficients satisfy a standard Lipschitz condition. For this class of systems, we then show the asymptotic separation property between two different solutions of Caputo SMTDEs with a more general condition based on λ. Furthermore, the asymptotic separation rate for the two distinct mild solutions reveals that our asymptotic results are general.
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Seangwattana T, Sombut K, Arunchai A, Sitthithakerngkiet K. A Modified Tseng’s Method for Solving the Modified Variational Inclusion Problems and Its Applications. Symmetry (Basel) 2021; 13:2250. [DOI: 10.3390/sym13122250] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
The goal of this study was to show how a modified variational inclusion problem can be solved based on Tseng’s method. In this study, we propose a modified Tseng’s method and increase the reliability of the proposed method. This method is to modify the relaxed inertial Tseng’s method by using certain conditions and the parallel technique. We also prove a weak convergence theorem under appropriate assumptions and some symmetry properties and then provide numerical experiments to demonstrate the convergence behavior of the proposed method. Moreover, the proposed method is used for image restoration technology, which takes a corrupt/noisy image and estimates the clean, original image. Finally, we show the signal-to-noise ratio (SNR) to guarantee image quality.
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Khan NA, Sulaiman M, Tavera Romero CA, Alarfaj FK. Numerical Analysis of Electrohydrodynamic Flow in a Circular Cylindrical Conduit by Using Neuro Evolutionary Technique. Energies 2021; 14:7774. [DOI: 10.3390/en14227774] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
This paper analyzes the mathematical model of electrohydrodynamic (EHD) fluid flow in a circular cylindrical conduit with an ion drag configuration. The phenomenon was modelled as a nonlinear differential equation. Furthermore, an application of artificial neural networks (ANNs) with a generalized normal distribution optimization algorithm (GNDO) and sequential quadratic programming (SQP) were utilized to suggest approximate solutions for the velocity, displacements, and acceleration profiles of the fluid by varying the Hartmann electric number (Ha2) and the strength of nonlinearity (α). ANNs were used to model the fitness function for the governing equation in terms of mean square error (MSE), which was further optimized initially by GNDO to exploit the global search. Then SQP was implemented to complement its local convergence. Numerical solutions obtained by the design scheme were compared with RK-4, the least square method (LSM), and the orthonormal Bernstein collocation method (OBCM). Stability, convergence, and robustness of the proposed algorithm were endorsed by the statistics and analysis on results of absolute errors, mean absolute deviation (MAD), Theil’s inequality coefficient (TIC), and error in Nash Sutcliffe efficiency (ENSE).
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Guran L, Mitrović ZD, Reddy GSM, Belhenniche A, Radenović S. Applications of a Fixed Point Result for Solving Nonlinear Fractional and Integral Differential Equations. Fractal Fract 2021; 5:211. [DOI: 10.3390/fractalfract5040211] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
In this article, we apply one fixed point theorem in the setting of b-metric-like spaces to prove the existence of solutions for one type of Caputo fractional differential equation as well as the existence of solutions for one integral equation created in mechanical engineering.
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Nagy AM, Makhlouf AB, Alsenafi A, Alazemi F. Combination Synchronization of Fractional Systems Involving the Caputo–Hadamard Derivative. Mathematics 2021; 9:2781. [DOI: 10.3390/math9212781] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
The main aim of this paper is to investigate the combination synchronization phenomena of various fractional-order systems using the scaling matrix. For this purpose, the combination synchronization is performed by considering two drive systems and one response system. We show that the combination synchronization phenomenon is achieved theoretically. Moreover, numerical simulations are carried out to confirm and validate the obtained theoretical results.
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Segovia-Martin J, Tamariz M. Synchronising institutions and value systems: A model of opinion dynamics mediated by proportional representation. PLoS One 2021; 16:e0257525. [PMID: 34582478 DOI: 10.1371/journal.pone.0257525] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2020] [Accepted: 09/06/2021] [Indexed: 11/19/2022] Open
Abstract
Individuals increasingly participate in online platforms where they copy, share and form they opinions. Social interactions in these platforms are mediated by digital institutions, which dictate algorithms that in turn affect how users form and evolve their opinions. In this work, we examine the conditions under which convergence on shared opinions can be obtained in a social network where connected agents repeatedly update their normalised cardinal preferences (i.e. value systems) under the influence of a non-constant reflexive signal (i.e. institution) that aggregates populations’ information using a proportional representation rule. We analyse the impact of institutions that aggregate (i) expressed opinions (i.e. opinion-aggregation institutions), and (ii) cardinal preferences (i.e. value-aggregation institutions). We find that, in certain regions of the parameter space, moderate institutional influence can lead to moderate consensus and strong institutional influence can lead to polarisation. In our randomised network, local coordination alone in the total absence of institutions does not lead to convergence on shared opinions, but very low levels of institutional influence are sufficient to generate a feedback loop that favours global conventions. We also show that opinion-aggregation may act as a catalyst for value change and convergence. When applied to digital institutions, we show that the best mechanism to avoid extremism is to increase the initial diversity of the value systems in the population.
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Fernsel P. Spatially Coherent Clustering Based on Orthogonal Nonnegative Matrix Factorization. J Imaging 2021; 7:jimaging7100194. [PMID: 34677280 PMCID: PMC8540947 DOI: 10.3390/jimaging7100194] [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: 08/19/2021] [Revised: 09/20/2021] [Accepted: 09/23/2021] [Indexed: 01/15/2023] Open
Abstract
Classical approaches in cluster analysis are typically based on a feature space analysis. However, many applications lead to datasets with additional spatial information and a ground truth with spatially coherent classes, which will not necessarily be reconstructed well by standard clustering methods. Motivated by applications in hyperspectral imaging, we introduce in this work clustering models based on Orthogonal Nonnegative Matrix Factorization (ONMF), which include an additional Total Variation (TV) regularization procedure on the cluster membership matrix to enforce the needed spatial coherence in the clusters. We propose several approaches with different optimization techniques, where the TV regularization is either performed as a subsequent post-processing step or included into the clustering algorithm. Finally, we provide a numerical evaluation of 12 different TV regularized ONMF methods on a hyperspectral dataset obtained from a matrix-assisted laser desorption/ionization imaging measurement, which leads to significantly better clustering results compared to classical clustering models.
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Affiliation(s)
- Pascal Fernsel
- Center for Industrial Mathematics, University of Bremen, 28359 Bremen, Germany
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