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SIAM Journal on Applied Mathematics
Journal Prestige (SJR): 1.108  Citation Impact (citeScore): 2 Number of Followers: 13  Hybrid journal * Containing 1  Open Access article(s) in this issue *ISSN (Print) 0036-1399 - ISSN (Online) 1095-712X Published by Society for Industrial and Applied Mathematics  [17 journals]
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- Maximizing Metapopulation Growth Rate and Biomass in Stream Networks
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Authors: Tung D. Nguyen, Yixiang Wu, Amy Veprauskas, Tingting Tang, Ying Zhou, Charlotte Beckford, Brian Chau, Xiaoyun Chen, Behzad Djafari Rouhani, Yuerong Wu, Yang Yang, Zhisheng Shuai
Pages: 2145 - 2168
Abstract: SIAM Journal on Applied Mathematics, Volume 83, Issue 6, Page 2145-2168, December 2023.
Abstract. We consider the logistic metapopulation model over a stream network and use the metapopulation growth rate and the total biomass (of the positive equilibrium) as metrics for different aspects of population persistence. Our objective is to find distributions of resources that maximize these persistence measures. We begin our study by considering stream networks consisting of three nodes and prove that the strategy to maximize the total biomass is to concentrate all the resources in the most upstream locations. In contrast, when the diffusion rates are sufficiently small, the metapopulation growth rate is maximized when all resources are concentrated in one of the most downstream locations. These two main results are generalized to stream networks with any number of patches.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-11-03T07:00:00Z
DOI: 10.1137/23M1556757
Issue No: Vol. 83, No. 6 (2023)
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- On Spatial Cohesiveness of Second-Order Self-Propelled Swarming Systems
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Authors: Constantine Medynets, Irina Popovici
Pages: 2169 - 2188
Abstract: SIAM Journal on Applied Mathematics, Volume 83, Issue 6, Page 2169-2188, December 2023.
Abstract. The study of emergent behavior of swarms is of great interest for applied sciences. One of the most fundamental questions for self-organizing swarms is whether the swarms disperse or remain in a spatially cohesive configuration. In this paper we study dissipativity properties and spatial cohesiveness of the swarm of self-propelled particles governed by the model [math], where [math], [math], and [math] is a symmetric positive semidefinite matrix. The self-propulsion term is assumed to be continuously differentiable and to grow faster than [math], that is, [math] as [math]. We establish that the velocity and acceleration of the particles are ultimately bounded. We show that when [math] is trivial, the positions of the particles are also ultimately bounded. For systems with [math], we show that, while the system might infinitely drift away from its initial location, the particles remain within a bounded distance from the generalized center of mass of the system, which geometrically coincides with the weighted average of agent positions. The weights are determined by the coefficients of the projection matrix onto [math]. We also discuss the ultimate boundedness for systems with bounded coupling, including the Morse potential systems, and systems governed by power-law potentials with strong repulsion properties. We show that the former systems are ultimately bounded in the velocity-acceleration domain, whereas the models based on the power-law potentials are not.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-11-09T08:00:00Z
DOI: 10.1137/23M1553388
Issue No: Vol. 83, No. 6 (2023)
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- Sliding-Mode Theory Under Feedback Constraints and the Problem of Epidemic
Control-
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Authors: Mauro Bisiacco, Gianluigi Pillonetto
Pages: 2189 - 2211
Abstract: SIAM Journal on Applied Mathematics, Volume 83, Issue 6, Page 2189-2211, December 2023.
Abstract. One of the most important branches of nonlinear control theory of dynamical systems is the so-called sliding mode. Its aim is the design of a (nonlinear) feedback law that brings and maintains the state trajectory of a dynamic system on a given sliding surface. Here, dynamics become completely independent of the model parameters and can be tuned accordingly to the desired target. In this paper we study this problem when the feedback law is subject to strong structural constraints. In particular, we assume that the control input may take values only over two bounded and disjoint sets. Such sets could be also not perfectly known a priori. An example is a control input allowed to switch only between two values. Under these peculiarities, we derive the necessary and sufficient conditions that guarantee sliding-mode control effectiveness for a class of time-varying continuous-time linear systems that includes all the stationary state-space linear models. Our analysis covers several scientific fields. It is only apparently confined to the linear setting and also allows one study an important set of nonlinear models. We describe fundamental examples related to epidemiology where the control input is the level of contact rate among people and the sliding surface permits to control the number of infected. We prove the global convergence of epidemic sliding-mode control schemes applied to two popular dynamical systems used in epidemiology, i.e., SEIR and SAIR, and based on the introduction of severe restrictions like lockdowns. Results obtained in the literature regarding control of many other epidemiological models are also generalized by casting them within a general sliding-mode theory.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-11-15T08:00:00Z
DOI: 10.1137/22M1535309
Issue No: Vol. 83, No. 6 (2023)
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- Global Dynamics and Pattern Formation in a Diffusive Population-Toxicant
Model with Negative Toxicant-Taxis-
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Authors: Xiumei Deng, Qihua Huang, Zhi-An Wang
Pages: 2212 - 2236
Abstract: SIAM Journal on Applied Mathematics, Volume 83, Issue 6, Page 2212-2236, December 2023.
Abstract. Because of the significance of remediating contaminated ecosystems, many mathematical models have been developed to describe the interactions between populations and toxicants in polluted aquatic environments. These models typically neglect the consequences of toxicant-induced behavioral changes on population dynamics. Taking into account that individuals may flee from areas with high toxicant concentrations to areas with low toxicant concentrations in order to improve their chances of survival, growth, and reproduction, we develop a diffusive population-toxicant model with toxicant-taxis. We establish the global well-posedness of our model and prove the global stability of spatially homogeneous toxicant-only steady states and population-toxicant coexistence steady states under some conditions. We find conditions under which stable spatially inhomogeneous steady states become unstable to trigger spatial pattern formations as the toxicant-taxis is strong. We also identify a narrow parameter regime in which toxicant-only and population-toxicant coexistence steady states are bistable. Numerical simulations are performed to illustrate that spatial aggregation and segregation patterns between the population and the toxicant will typically emerge. Our study highlights the important effects of toxicant-induced movement responses on the spatial distributions of populations in polluted aquatic environments.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-11-15T08:00:00Z
DOI: 10.1137/22M1510881
Issue No: Vol. 83, No. 6 (2023)
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- Power-Engine-Load Form for Dynamic Absolute Concentration Robustness
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Authors: Badal Joshi, Gheorghe Craciun
Pages: 2237 - 2259
Abstract: SIAM Journal on Applied Mathematics, Volume 83, Issue 6, Page 2237-2259, December 2023.
Abstract. In a reaction network, the concentration of a species with the property of dynamic absolute concentration robustness (dynamic ACR) converges to the same value independent of the overall initial values. This property endows a biochemical network with output robustness and therefore is essential for its functioning in a highly variable environment. It is important to identify the structure of the dynamical system as well as the constraints required for dynamic ACR. We propose a power-engine-load form of dynamic ACR and obtain results regarding convergence to the ACR value based on this form.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-11-20T08:00:00Z
DOI: 10.1137/22M1535450
Issue No: Vol. 83, No. 6 (2023)
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- Prevalence of Multistationarity and Absolute Concentration Robustness in
Reaction Networks-
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Authors: Badal Joshi, Nidhi Kaihnsa, Tung D. Nguyen, Anne Shiu
Pages: 2260 - 2283
Abstract: SIAM Journal on Applied Mathematics, Volume 83, Issue 6, Page 2260-2283, December 2023.
Abstract. For reaction networks arising in systems biology, the capacity for two or more steady states, that is, multistationarity, is an important property that underlies biochemical switches. Another property receiving much attention recently is absolute concentration robustness (ACR), which means that some species concentration is the same at all positive steady states. In this work, we investigate the prevalence of each property while paying close attention to when the properties occur together. Specifically, we consider a stochastic block framework for generating random networks and prove edge-probability thresholds at which, with high probability, multistationarity appears and ACR becomes rare. We also show that the small window in which both properties occur only appears in networks with many species. Taken together, our results confirm that, in random reversible networks, ACR and multistationarity together, or even ACR on its own, is highly atypical. Our proofs rely on two prior results, one pertaining to the prevalence of networks with deficiency zero and the other “lifting” multistationarity from small networks to larger ones.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-11-20T08:00:00Z
DOI: 10.1137/23M1549316
Issue No: Vol. 83, No. 6 (2023)
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- A Multifaceted Study of Nematic Order Reconstruction in Microfluidic
Channels-
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Authors: James Dalby, Yucen Han, Apala Majumdar, Lidia Mrad
Pages: 2284 - 2309
Abstract: SIAM Journal on Applied Mathematics, Volume 83, Issue 6, Page 2284-2309, December 2023.
Abstract. We study order reconstruction (OR) solutions in the Beris–Edwards framework for nematodynamics, for both passive and active nematic flows in a microfluidic channel. OR solutions exhibit polydomains and domain walls, and as such, are of physical interest. We show that OR solutions exist for passive flows with constant velocity and pressure, but only for specific boundary conditions. We prove the existence of unique, symmetric, and nonsingular nematic profiles for boundary conditions that do not allow for OR solutions. We compute asymptotic expansions for OR-type solutions for passive flows with nonconstant velocity and pressure, and active flows, which shed light on the internal structure of domain walls. The asymptotics are complemented by numerical studies that demonstrate the universality of OR-type structures in static and dynamic scenarios.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-11-27T08:00:00Z
DOI: 10.1137/22M1490909
Issue No: Vol. 83, No. 6 (2023)
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- A Density Description of a Bounded-Confidence Model of Opinion Dynamics on
Hypergraphs-
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Authors: Weiqi Chu, Mason A. Porter
Pages: 2310 - 2328
Abstract: SIAM Journal on Applied Mathematics, Volume 83, Issue 6, Page 2310-2328, December 2023.
Abstract. Social interactions often occur between three or more agents simultaneously. Examining opinion dynamics on hypergraphs allows one to study the effect of such polyadic interactions on the opinions of agents. In this paper, we consider a bounded-confidence model (BCM), in which opinions take continuous values and interacting agents comprise their opinions if they are close enough to each other. We study a density description of a Deffuant–Weisbuch BCM on hypergraphs. We derive a rate equation for the mean-field opinion density as the number of agents becomes infinite, and we prove that this rate equation yields a probability density that converges to noninteracting opinion clusters. Using numerical simulations, we examine bifurcations of the density-based BCM’s steady-state opinion clusters and demonstrate that the agent-based BCM converges to the density description of the BCM as the number of agents becomes infinite.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-11-28T08:00:00Z
DOI: 10.1137/22M148608X
Issue No: Vol. 83, No. 6 (2023)
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- Hypernetworks: Cluster Synchronization Is a Higher-Order Effect
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Authors: Sören von der Gracht, Eddie Nijholt, Bob Rink
Pages: 2329 - 2353
Abstract: SIAM Journal on Applied Mathematics, Volume 83, Issue 6, Page 2329-2353, December 2023.
Abstract. Many networked systems are governed by non-pairwise interactions between nodes. The resulting higher-order interaction structure can then be encoded by means of a hypernetwork. In this paper we consider dynamical systems on hypernetworks by defining a class of admissible maps for every such hypernetwork. We explain how to classify robust cluster synchronization patterns on hypernetworks by finding balanced partitions, and we generalize the concept of a graph fibration to the hypernetwork context. We also show that robust synchronization patterns are only fully determined by polynomial admissible maps of high order. This means that, unlike in dyadic networks, cluster synchronization on hypernetworks is a higher-order, i.e., nonlinear, effect. We give a formula, in terms of the order of the hypernetwork, for the degree of the polynomial admissible maps that determine robust synchronization patterns. We also demonstrate that this degree is optimal by investigating a class of examples. We conclude by demonstrating how this effect may cause remarkable synchrony breaking bifurcations that occur at high polynomial degree.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-11-28T08:00:00Z
DOI: 10.1137/23M1561075
Issue No: Vol. 83, No. 6 (2023)
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- Multiscale Modeling and Analysis of Growth of Plant Tissues
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Authors: Arezki Boudaoud, Annamaria Kiss, Mariya Ptashnyk
Pages: 2354 - 2389
Abstract: SIAM Journal on Applied Mathematics, Volume 83, Issue 6, Page 2354-2389, December 2023.
Abstract. How morphogenesis depends on cell properties is an active direction of research. Here, we focus on mechanical models of growing plant tissues, where microscopic (sub)cellular structure is taken into account. In order to establish links between microscopic and macroscopic tissue properties, we perform a multiscale analysis of a model of growing plant tissue with subcellular resolution. We use homogenization to rigorously derive the corresponding macroscopic tissue-scale model. Tissue-scale mechanical properties are computed from microscopic structural and material properties, taking into account deformation by the growth field. We then consider case studies and numerically compare the detailed microscopic model and the tissue-scale model, both implemented using the finite element method. We find that the macroscopic model can be used to efficiently make predictions about several configurations of interest. Our work will help making links between microscopic measurements and macroscopic observations in growing tissues.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-11-29T08:00:00Z
DOI: 10.1137/23M1553315
Issue No: Vol. 83, No. 6 (2023)
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- Homogenization for a Variational Problem with a Slip Interface Condition
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Authors: Miao-jung Yvonne Ou, Silvia Jiménez Bolaños
Pages: 2390 - 2417
Abstract: SIAM Journal on Applied Mathematics, Volume 83, Issue 6, Page 2390-2417, December 2023.
Abstract. Inspired by applications, we study the effect of interface slip on the effective wave propagation in poroelastic materials, which are composites consisting of elastic frames whose pore space is filled with fluid. The current literature on the homogenization for the poroelastic wave equations are all based on the no-slip interface condition posed on the microscale. However, for certain pore fluids, the no-slip condition is known to be physically invalid. In the literature, slip boundary conditions have been considered for porous materials with rigid solid frames. For these rigid porous materials, the wave can only propagate in the pore fluid and hence the equations for the microscale are posed only in the pore space. Consequently, the slip on the interface involves only the fluid velocity and the fluid stress. In contrast, for poroelastic materials, the wave can propagate not only in the pore fluid but also in the solid frame; hence the slip conditions involve the velocities on both sides of the interface, rather than just the fluid side. With this slip condition, a variational boundary value problem governing the small vibrations of a periodic mixture of an elastic solid and a slightly viscous fluid is studied in this paper. The method of two-scale convergence is used to obtain the macroscopic behavior of the solution and to identify the role played by the slip interface condition.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-11-30T08:00:00Z
DOI: 10.1137/22M1506961
Issue No: Vol. 83, No. 6 (2023)
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- Neuronal Resilience and Calcium Signaling Pathways in the Context of
Synapse Loss and Calcium Leaks: A Computational Modeling Study and
Implications for Alzheimer’s Disease-
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Authors: Piyush R. Borole, James M. Rosado, MeiRose Neal, Gillian Queisser
Pages: 2418 - 2442
Abstract: SIAM Journal on Applied Mathematics, Volume 83, Issue 6, Page 2418-2442, December 2023.
Abstract. In this paper, a coupled electro-calcium model was developed and implemented to computationally explore the effects of neuronal synapse loss, in particular in the context of Alzheimer’s disease. Established parameters affected by Alzheimer’s disease, such as synapse loss, calcium leaks at deteriorating synaptic contacts, and downregulation of the calcium buffer calbindin, are subject to this study. Reconstructed neurons are used to define the computational domain for a system of PDEs and ODEs, discretized by finite differences and solved with a semi-implicit second-order time integrator. The results show neuronal resilience during synapse loss. When incorporating calcium leaks at affected synapses, neurons lose their ability to produce synapse-to-nucleus calcium signals, necessary for learning, plasticity, and neuronal survival. Downregulation of calbindin concentrations partially recovers the signaling pathway to the cell nucleus. These results could define future research pathways toward stabilizing the calcium signaling pathways during Alzheimer’s disease. The coupled electro-calcium model was implemented and solved using MATLAB https://github.com/NeuroBox3D/CalcSim.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-12-05T08:00:00Z
DOI: 10.1137/23M1557842
Issue No: Vol. 83, No. 6 (2023)
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- Design of Defected Non-hermitian Chains of Resonator Dimers for Spatial
and Spatio-temporal Localizations-
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Authors: Habib Ammari, Erik Orvehed Hiltunen, Thea Kosche
Pages: 2443 - 2468
Abstract: SIAM Journal on Applied Mathematics, Volume 83, Issue 6, Page 2443-2468, December 2023.
Abstract. The aim of this article is to advance the field of metamaterials by proposing formulas for the design of high-contrast metamaterials with prescribed subwavelength defect mode eigenfrequencies. This is achieved in two settings: (i) design of non-Hermitian static materials and (ii) design of instantly changing non-Hermitian time-dependent materials. The design of static materials is achieved via characterizing equations for the defect mode eigenfrequencies in the setting of a defected dimer material. These characterizing equations are the basis for obtaining formulas for the material parameters of the defect which admit given defect mode eigenfrequencies. Explicit formulas are provided in the setting of one and two given defect mode eigenfrequencies in the setting of a defected chain of dimers. In the time-dependent case, we first analyze the influence of time boundaries on the subwavelength solutions. We find that subwavelength solutions are preserved if and only if the material parameters satisfy a temporal Snell’s law across the time boundary. The same result also identifies the change of the time frequencies uniquely. Combining this result with those on the design of static materials, we obtain an explicit formula for the material design of instantly changing defected dimer materials which admit subwavelength modes with prescribed time-dependent defect mode eigenfrequency. Finally, we use this formula to create materials which admit spatio-temporally localized defect modes.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-12-05T08:00:00Z
DOI: 10.1137/23M1573896
Issue No: Vol. 83, No. 6 (2023)
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- Spectral Patterns of Elastic Transmission Eigenfunctions: Boundary
Localization, Surface Resonance, and Stress Concentration-
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Authors: Yan Jiang, Hongyu Liu, Jiachuan Zhang, Kai Zhang
Pages: 2469 - 2498
Abstract: SIAM Journal on Applied Mathematics, Volume 83, Issue 6, Page 2469-2498, December 2023.
Abstract. We present a comprehensive study of new discoveries on the spectral patterns of elastic transmission eigenfunctions, including boundary localization, surface resonance, and stress concentration. In the case where the domain is radial and the underlying parameters are constant, we give rigorous justifications and derive a thorough understanding of those intriguing geometric and physical patterns. We also present numerical examples to verify that the same results hold in general geometric and parameter setups.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-12-05T08:00:00Z
DOI: 10.1137/22M1538417
Issue No: Vol. 83, No. 6 (2023)
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- Modeling Acoustic Space-Coiled Metacrystals
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Authors: Joar Zhou Hagström, Kim Pham, Agnés Maurel
Pages: 2499 - 2521
Abstract: SIAM Journal on Applied Mathematics, Volume 83, Issue 6, Page 2499-2521, December 2023.
Abstract. We present an effective model of “space-coiled metacrystals” composed of a periodic array of sound rigid blocks into which long slots have been coiled up. The periodic cell of the block contains a coiled slot whose straight parts are at wavelength scale, which enables the appearance of Bragg resonances. These resonances, which prevent high transmission, compete with the Fabry–Pérot resonances of the entire slot, which foster perfect transmission. This results in complex scattering properties driven by the characteristics of the turning regions that act as atoms in a one-dimensional coiled crystal. Using appropriate scaling and combining two-scale homogenization with matched asymptotic techniques, the modeling of such metacrystals is proposed. The resulting model is validated through a comparison with full-wave numerics in both harmonic and transient regimes.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-12-06T08:00:00Z
DOI: 10.1137/22M1527131
Issue No: Vol. 83, No. 6 (2023)
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- Analysis on a Spatial SIS Epidemic Model with Saturated Incidence Function
in Advective Environments: I. Conserved Total Population-
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Authors: Xiaodan Chen, Renhao Cui
Pages: 2522 - 2544
Abstract: SIAM Journal on Applied Mathematics, Volume 83, Issue 6, Page 2522-2544, December 2023.
Abstract. This paper concerns the qualitative analysis on a reaction-diffusion SIS (susceptible-infected-susceptible) epidemic model governed by the saturated incidence infection mechanism in advective environments. A variational expression of the basic reproduction number [math] was derived and the global dynamics of the system in terms of [math] was established: the disease-free equilibrium is unique and linearly stable if [math] and at least an endemic equilibrium exists if [math]. More precisely, we explore qualitative properties of the basic reproduction number and investigate the spatial distribution of the individuals with respect to the dispersal and advection. We find that the concentration phenomenon occurs when the advection is large and the infectious disease will be eradicated for the small dispersal of infected individual. Our theoretical results may shed some new insight into the infectious disease prediction and control strategy.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-12-08T08:00:00Z
DOI: 10.1137/22M1534699
Issue No: Vol. 83, No. 6 (2023)
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- Pattern Formation and Oscillations in Nonlinear Random Walks on Networks
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Authors: Per Sebastian Skardal
Pages: 1767 - 1784
Abstract: SIAM Journal on Applied Mathematics, Volume 83, Issue 5, Page 1767-1784, October 2023.
Abstract. Random walks represent an important tool for probing the structural and dynamical properties of networks and modeling transport and diffusion processes on networks. However, when individuals’ movements become dictated by more complicated factors, e.g., scenarios that involve complex decision making, the linear paradigm of classical random walks lacks the ability to capture dynamically rich behaviors. One modification that addresses this issue is to allow transition probabilities to depend on the current system state, resulting in a nonlinear random walk. While the resulting nonlinearity has been shown to give rise to an array of more complex dynamics, the patterns that emerge, in particular on regular network topologies, remain unexplored and poorly understood. Here we study nonlinear random walks on regular networks. We present a number of stability results for the uniform state where random walkers are uniformly distributed throughout the network, characterizing the spectral properties of its Jacobian which we use to characterize its bifurcations. These spectral properties may also be used to understand the patterns that emerge beyond bifurcations, which consist of oscillating short wavelength patterns and localized structures for negative and positive bias, respectively. We also uncover a subcriticality in the bifurcation for positive bias, leading to a hysteresis loop and multistability.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-09-14T07:00:00Z
DOI: 10.1137/22M1536662
Issue No: Vol. 83, No. 5 (2023)
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- A PML Method for Signal-Propagation Problems in Axon
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Authors: Xue Jiang, Maohui Lyu, Tao Yin, Weiying Zheng
Pages: 1785 - 1805
Abstract: SIAM Journal on Applied Mathematics, Volume 83, Issue 5, Page 1785-1805, October 2023.
Abstract. This work is focused on the modeling of signal propagations in myelinated axons to characterize the functions of the myelin sheath in the neural structure. Based on reasonable assumptions on the medium properties, we derive a two-dimensional neural-signaling model in cylindrical coordinates from the time-harmonic Maxwell equations. The well-posedness of the model is established upon Dirichlet boundary conditions at the two ends of the neural structure and the radiative condition in the radial direction of the structure. Using the perfectly matched layer (PML) method, we truncate the unbounded background medium and propose an approximate problem on the truncated domain. The well-posedness of the PML problem and the exponential convergence of the approximate solution to the exact solution are established. Numerical experiments based on finite element discretization are presented to demonstrate the theoretical results and the efficiency of our methods of simulating the signal propagation in axons.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-09-14T07:00:00Z
DOI: 10.1137/22M1544063
Issue No: Vol. 83, No. 5 (2023)
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- Basic Reproduction Ratios for Time-Periodic Homogeneous Evolution Systems
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Authors: Feng-Bin Wang, Lei Zhang, Xiao-Qiang Zhao
Pages: 1806 - 1831
Abstract: SIAM Journal on Applied Mathematics, Volume 83, Issue 5, Page 1806-1831, October 2023.
Abstract. This paper is devoted to the study of basic reproduction ratios [math] for time-periodic homogeneous evolution systems. We introduce the definition of [math] and show that the sign of [math] determines the stability of the zero solution for such a system. We also characterize [math] and give a numerical method to compute it. Then we apply the developed theory to two population models and obtain threshold type results on their global dynamics in terms of [math].
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-09-15T07:00:00Z
DOI: 10.1137/22M1531865
Issue No: Vol. 83, No. 5 (2023)
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- Minimizing Congestion in Single-Source, Single-Sink Queueing Networks
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Authors: Fabian Ying, Alisdair O. G. Wallis, Mason A. Porter, Sam D. Howison, Mariano Beguerisse-Díaz
Pages: 1832 - 1853
Abstract: SIAM Journal on Applied Mathematics, Volume 83, Issue 5, Page 1832-1853, October 2023.
Abstract. Motivated by the modeling of customer mobility and congestion in supermarkets, we study queueing networks with a single source and a single sink. We assume that walkers traverse a network according to an unbiased random walk, and we analyze how network topology affects the total mean queue size [math], which we use to measure congestion. We examine network topologies that minimize [math] and provide proofs of optimality for some cases and numerical evidence of optimality for others. Finally, we present greedy algorithms that add edges to and delete edges from a network to reduce [math], and we apply these algorithms to a network that we construct using a supermarket store layout. We find that these greedy algorithms, which typically tend to add edges to the sink node, are able to significantly reduce [math]. Our work helps improve understanding of how to design networks with low congestion and how to amend networks to reduce congestion.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-09-15T07:00:00Z
DOI: 10.1137/21M1457515
Issue No: Vol. 83, No. 5 (2023)
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- The BCC Lattice in a Long-Range Interaction System
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Authors: Xiaofeng Ren, Juncheng Wei
Pages: 1854 - 1871
Abstract: SIAM Journal on Applied Mathematics, Volume 83, Issue 5, Page 1854-1871, October 2023.
Abstract. While the hexagonal lattice is ubiquitous in two dimensions, the body centered cubic lattice (BCC lattice) and the face centered cubic lattice are both commonly observed in three dimensions. A geometric variational problem motivated by the diblock copolymer theory consists of a short-range interaction energy and a long-range interaction energy. In three dimensions, and when the long range interaction is given by the nonlocal operator [math], it is proved that the BCC lattice is the preferred structure.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-09-19T07:00:00Z
DOI: 10.1137/22M1511722
Issue No: Vol. 83, No. 5 (2023)
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- Uncovering a Two-Phase Dynamics from a Dollar Exchange Model with Bank and
Debt-
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Authors: Fei Cao, Sébastien Motsch
Pages: 1872 - 1891
Abstract: SIAM Journal on Applied Mathematics, Volume 83, Issue 5, Page 1872-1891, October 2023.
Abstract. We investigate the unbiased model for money exchanges with collective debt limit: agents give at random time a dollar to one another as long as they have at least one dollar or they can borrow a dollar from a central bank if the bank is not empty. Surprisingly, this dynamic eventually leads to an asymmetric Laplace distribution of wealth (conjectured in [N. Xi, N. Ding, and Y. Wang, Phys. A, 357 (2005), pp. 543–555] and shown formally in a recent work [N. Lanchier and S. Reed, J. Stat. Phys., 176 (2019), pp. 1115–1137]). In this manuscript, we carry out a formal mean-field limit as the number of agents goes to infinity where we uncover a two-phase ODE dynamic. Convergence towards the unique equilibrium (two-sided geometric) distribution in the large time limit is also shown and the role played by the bank and debt (in terms of Gini index or wealth inequality) will be explored numerically as well.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-09-20T07:00:00Z
DOI: 10.1137/22M1518621
Issue No: Vol. 83, No. 5 (2023)
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- Bifurcation Analysis in a Tumor-Immune System Interaction Model with
Dendritic Cell Therapy and Immune Response Delay-
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Authors: Yuyue Zhang, Liqi Xie, Yueping Dong, Jicai Huang, Shigui Ruan, Yasuhiro Takeuchi
Pages: 1892 - 1914
Abstract: SIAM Journal on Applied Mathematics, Volume 83, Issue 5, Page 1892-1914, October 2023.
Abstract. In this paper, we study a tumor-immune system interaction model with dendritic cell therapy and immune response delay. First, it is shown that the ODE version of the model has a Bogdanov–Takens (BT) singularity or a weak focus with multiplicity at most 1 for different parameter values. As the parameters vary, the ODE model undergoes supercritical Hopf bifurcation and supercritical BT bifurcation. Our analysis indicates that there exists a threshold value of the activation rate of T cells, below which tumor immune escape occurs, above or at which T cells and tumor cells coexist in the form of a stable periodic oscillation or steady state. Second, we study how the immune response delay affects the dynamics of the model. Our results reveal that the delay can destabilize the stable positive equilibrium through Hopf bifurcation. Furthermore, the direction and stability of Hopf bifurcation are derived. When there is a cusp, we show that it is a BT singularity for any delay and the delay model also undergoes BT bifurcation. Finally, numerical simulations are presented to illustrate the theoretical results.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-09-21T07:00:00Z
DOI: 10.1137/22M1533979
Issue No: Vol. 83, No. 5 (2023)
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- Reconstruction of Multiscale Elastic Sources from Multifrequency Sparse
Far Field Patterns-
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Authors: Jialei Li, Xiaodong Liu, Qingxiang Shi
Pages: 1915 - 1934
Abstract: SIAM Journal on Applied Mathematics, Volume 83, Issue 5, Page 1915-1934, October 2023.
Abstract. We consider the inverse time-harmonic elastic source problems with multifrequency sparse far field patterns. The unknown multiscale object is a combination of point sources and an extended source with compact support. Even if the extended source is unknown, we prove that the locations and the polarization strengths of the point sources can be uniquely determined by the multifrequency far field patterns at sparse observations. The least number of observation directions is given in terms of the number of the point sources. Having identified the point sources, under certain conditions, we further show that the multifrequency far field patterns at a fixed observation direction uniquely determine the narrowest strip containing the source support. With the increase of the number of observation directions, a convex hull of the source support can be obtained. Based on the constructive uniqueness proof, we introduce a novel direct sampling method both for locating the point sources and for reconstructing the support of the extended source. A formula for computing the polarization strengths is also given. Numerical examples in two dimensions are presented to verify the accuracy and robustness of the proposed methods for multiscale elastic sources.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-09-22T07:00:00Z
DOI: 10.1137/22M1544257
Issue No: Vol. 83, No. 5 (2023)
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- Analysis of the Lévy Flight Foraging Hypothesis in [math] and
Unreliability of the Most Rewarding Strategies-
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Authors: Serena Dipierro, Giovanni Giacomin, Enrico Valdinoci
Pages: 1935 - 1968
Abstract: SIAM Journal on Applied Mathematics, Volume 83, Issue 5, Page 1935-1968, October 2023.
Abstract. We analyze the searching strategies of a forager diffusing in the whole space via an equation of fractional type. Specifically, the diffusion of the forager is regulated by a Lévy flight whose exponent can be chosen in order to optimize a suitable foraging efficiency functional. Here, the dimension of the space is arbitrary. On the one hand, we show that the exponent [math] corresponding to the limit case of heavy-tailed Lévy flights is a pessimizer for the efficiency functional. On the other hand, we prove that, in situations of biological interest, one finds the most rewarding strategies arbitrarily close to [math]. The combination of these results gives that the most rewarding searching option may turn out to be unfeasible, or at least unreliable, in practice, since small perturbations of the optimal searching exponent lead to pessimal patterns. The cases analyzed specifically are those of a target located in the proximity of the forager and that of sparse prey modeled by a target infinitely far from the initial position of the seeker. The efficiency functionals taken into account are either of pointwise type (in which the predator and the prey are modeled by moving points) or of set-dependent type (in which the predator and the prey correspond to regions of space with uniform density, thus modeling also the case of a sight range of the biological individuals involved). To implement our analysis, we also provide a number of structural results about finiteness, continuity, and asymptotic behaviors of the efficiency functionals. It is suggestive to relate the adoption of the most rewarding searching pattern close to pessimizers to a “high-risk/high-gain” strategy, in which the forager aims at high-energy content prey to mitigate the risk of failure. This setting is also connected to foraging modes of “ambush” type.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-09-25T07:00:00Z
DOI: 10.1137/22M1526563
Issue No: Vol. 83, No. 5 (2023)
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- Analysis of a Reaction-Diffusion SIR Epidemic Model with Noncompliant
Behavior-
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Authors: Christian Parkinson, Weinan Wang
Pages: 1969 - 2002
Abstract: SIAM Journal on Applied Mathematics, Volume 83, Issue 5, Page 1969-2002, October 2023.
Abstract. Recent work by public health experts suggests that incorporating human behavior is crucial in faithfully modeling an epidemic. We present a reaction-diffusion partial differential equation SIR-type population model for an epidemic including behavioral concerns. In our model, the disease spreads via mass action, as is customary in compartmental models. However, drawing from social contagion theory, we assume that as the disease spreads and prevention measures are enacted, noncompliance with prevention measures also spreads throughout the population. We prove global existence of classical solutions of our model, and then perform [math]-type analysis and determine asymptotic behavior of the model in different parameter regimes. Finally, we simulate the model and discuss the new facets which distinguish our model from basic SIR-type models.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-10-06T07:00:00Z
DOI: 10.1137/23M1556691
Issue No: Vol. 83, No. 5 (2023)
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- Data-Driven Basis for Reconstructing the Contrast in Inverse Scattering:
Picard Criterion, Regularity, Regularization, and Stability-
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Authors: Shixu Meng
Pages: 2003 - 2026
Abstract: SIAM Journal on Applied Mathematics, Volume 83, Issue 5, Page 2003-2026, October 2023.
Abstract. We consider the inverse medium scattering of reconstructing the medium contrast using Born data, including the full-aperture, limited-aperture, and multifrequency data. We propose data-driven basis functions for these inverse problems based on the generalized prolate spheroidal wave functions and related eigenfunctions. Such data-driven eigenfunctions are eigenfunctions of a Fourier integral operator; they remarkably extend analytically to the whole space, are doubly orthogonal, and are complete in the class of band-limited functions. We first establish a Picard criterion for reconstructing the contrast using the data-driven basis, where the reconstruction formula can also be understood from the viewpoint of data processing and analytic extrapolation. Another salient feature associated with the generalized prolate spheroidal wave functions is that the data-driven basis for a disk is also a basis for a Sturm–Liouville differential operator. With the help of Sturm–Liouville theory, we estimate the [math] approximation error for a spectral cutoff approximation of [math] functions. This yields a spectral cutoff regularization strategy for noisy data and an explicit stability estimate for contrast in [math] ([math]) in the full-aperture case. In the limited-aperture and multifrequency cases, we also obtain spectral cutoff regularization strategies for noisy data and stability estimates for a class of contrast.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-10-16T07:00:00Z
DOI: 10.1137/23M1545409
Issue No: Vol. 83, No. 5 (2023)
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- Similarity Suppresses Cyclicity: Why Similar Competitors Form Hierarchies
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Authors: Christopher Cebra, Alexander Strang
Pages: 2027 - 2051
Abstract: SIAM Journal on Applied Mathematics, Volume 83, Issue 5, Page 2027-2051, October 2023.
Abstract. Competitive systems can exhibit both hierarchical (transitive) and cyclic (intransitive) structures. Despite theoretical interest in cyclic competition, which offers richer dynamics and occupies a larger subset of the scope of possible competitive systems, most real-world systems are predominantly transitive. Why' Here, we introduce a generic mechanism that promotes transitivity, even when there is ample room for cyclicity. We demonstrate that, if competitive outcomes depend smoothly on competitor attributes, then similar competitors compete transitively. We quantify the rate of convergence to transitivity given the similarity of the competitors and the smoothness of the performance function. Thus, we prove the adage regarding apples and oranges. Similar objects admit well-ordered comparisons; diverse objects may not.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-10-17T07:00:00Z
DOI: 10.1137/22M1503099
Issue No: Vol. 83, No. 5 (2023)
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- Derivation and Stability Analysis of a Macroscopic Multilane Model for
Traffic Flow-
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Authors: Matteo Piu, Michael Herty, Gabriella Puppo
Pages: 2052 - 2072
Abstract: SIAM Journal on Applied Mathematics, Volume 83, Issue 5, Page 2052-2072, October 2023.
Abstract. The mathematical modeling and the stability analysis of multilane traffic in the macroscopic scale is considered. We propose a new first order model derived from microscopic dynamics with lane changing, leading to a coupled system of hyperbolic balance laws. The macroscopic limit is derived without assuming ad hoc space and time scalings. The analysis of the stability of the equilibria of the model is discussed. The proposed numerical tests confirm the theoretical findings between the macroscopic and microscopic modeling, and the results of the stability analysis.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-10-18T07:00:00Z
DOI: 10.1137/22M1543288
Issue No: Vol. 83, No. 5 (2023)
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- Reconstruction of an Interface Between the Fluid and Piezoelectric Solid
by Acoustic Measurements-
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Authors: Chengyu Wu, Jiaqing Yang
Pages: 2073 - 2095
Abstract: SIAM Journal on Applied Mathematics, Volume 83, Issue 5, Page 2073-2095, October 2023.
Abstract. In this paper, we consider an inverse interaction scattering problem of recovering an interface between the fluid and piezoelectric solid from acoustic measurements. First, the well-posedness of the interaction model is shown in associated function spaces by the variational method. Then new uniqueness results are proved for the inverse problem by taking far-field data at one fixed frequency, based on a uniform a priori estimate of the solutions of the interaction model. With these results, the factorization method is then justified to reconstruct the shape and location of the interface between the fluid and piezoelectric solid. Finally, we investigate an associated interior transmission eigenvalue problem, and show that the set of interior transmission eigenvalues is at most discrete and with no finite accumulation point under a natural assumption on physical coefficients.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-10-20T07:00:00Z
DOI: 10.1137/22M1519146
Issue No: Vol. 83, No. 5 (2023)
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- Phenotype Switching in Chemotaxis Aggregation Models Controls the
Spontaneous Emergence of Large Densities-
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Authors: Kevin J. Painter, Michael Winkler
Pages: 2096 - 2117
Abstract: SIAM Journal on Applied Mathematics, Volume 83, Issue 5, Page 2096-2117, October 2023.
Abstract. We consider a phenotype-switching chemotaxis model for aggregation, in which a chemotactic population is capable of switching back and forth between a chemotaxing state (performing chemotactic movement) and a secreting state (producing the attractant). We show that the switching rate provides a powerful mechanism for controlling the densities of spontaneously emerging aggregates. Specifically, in two- and three-dimensional settings it is shown that when both switching rates coincide and are suitably large, the densities of both the chemotaxing and the secreting populations will exceed any prescribed level at some points in the considered domain. This is complemented by two results asserting the absence of such aggregation phenomena in corresponding scenarios in which one of the switching rates remains within some bounded interval.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-10-24T07:00:00Z
DOI: 10.1137/22M1539393
Issue No: Vol. 83, No. 5 (2023)
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- A Homogenized Model of Fluid-String Interaction
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Authors: A. Kent, S. L. Waters, J. Oliver, S. J. Chapman
Pages: 2118 - 2143
Abstract: SIAM Journal on Applied Mathematics, Volume 83, Issue 5, Page 2118-2143, October 2023.
Abstract. A homogenized model is developed to describe the interaction between aligned strings and an incompressible, viscous, Newtonian fluid. In the case of many strings, the ratio of string separation to domain width gives a small parameter which can be exploited to simplify the problem. Model derivation using multiscale asymptotics results in a modified Darcy law for fluid flow, with coefficients determined by averaged solutions to microscale problems. Fluid flow is coupled to solid deformation via a homogenized force balance obtained by coarse-graining the balance on each string. This approach offers an alternative method to systematically derive the equations governing the interaction of Stokes flow with many flexible structures. The resulting model of fluid-structure interaction is reduced to a single scalar, linear, partial differential equation by introducing a potential for the pressure. Analytical solutions are presented for a cylindrical geometry subject to time-harmonic motion of the string ends. Scaling laws are identified that describe the variation of shear stress exerted on the string surface with the forcing frequency.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-10-24T07:00:00Z
DOI: 10.1137/22M1485929
Issue No: Vol. 83, No. 5 (2023)
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- Cell Polarity and Movement with Reaction-Diffusion and Moving Boundary:
Rigorous Model Analysis and Robust Simulations-
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Authors: Shuang Liu, Li-Tien Cheng, Bo Li
Pages: S515 - S537
Abstract: SIAM Journal on Applied Mathematics, Ahead of Print.
Abstract. Cell polarity and movement are fundamental to many biological functions. Experimental and theoretical studies have indicated that interactions of certain proteins lead to the cell polarization which plays a key role in controlling the cell movement. We study the cell polarity and movement based on a class of biophysical models that consist of reaction-diffusion equations for different proteins and the dynamics of a moving cell boundary. Such a moving boundary is often simulated by a phase-field model. We first apply the matched asymptotic analysis to give a rigorous derivation of the sharp-interface model of the cell boundary from a phase-field model. We then develop a robust numerical approach that combines the level-set method to track the sharp boundary of a moving cell and accurate discretization techniques for solving the reaction-diffusion equations on the moving cell region. Our extensive numerical simulations predict the cell polarization under various kinds of stimuli and capture both the linear and the circular trajectories of a moving cell for a long period of time. In particular, we have identified some key parameters controlling different cell trajectories that are less accurately predicted by reduced models. Our work has linked different models and also developed tools that can be adapted for the challenging three-dimensional simulations.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-11-16T08:00:00Z
DOI: 10.1137/22M1506766
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- Detecting and Resetting Tipping Points to Create More HIV Post-Treatment
Controllers with Bifurcation and Sensitivity Analysis-
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Authors: Wenjing Zhang, Leif A. Ellingson
Pages: S493 - S514
Abstract: SIAM Journal on Applied Mathematics, Ahead of Print.
Abstract. The existence of HIV post-treatment controllers (PTCs) offers hope for an HIV functional cure, and understanding the critical mechanisms determining PTC represents a key step toward this goal. Here, we have studied these mechanisms by analyzing an established mathematical model for HIV viral dynamics. In mathematical models, critical mechanisms are represented by parameters that affect the tipping points to induce qualitatively different dynamics, and in cases with multiple stability, the initial conditions of the system also play a role in determining the fate of the solution. As such, for the tipping points in parameter space, we developed and implemented a sensitivity analysis of the threshold conditions of the associated bifurcations to identify the critical mechanisms for this model. Our results suggest that the infected cell death rate and the saturation parameter for cytotoxic T lymphocyte proliferation significantly affect post-treatment control. For the case with multiple stability, in state space of initial conditions, we first investigated the saddle-type equilibrium point to identify its stable manifold, which delimits trapping regions associated to the high and low viral set points. The identified stable manifold serves as a guide for the loads of immune cells and HIV virus at the time of therapy termination to achieve post-treatment control.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-11-15T08:00:00Z
DOI: 10.1137/22M1485255
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- Fast Solver for Diffusive Transport Times on Dynamic Intracellular
Networks-
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Authors: Lachlan Elam, Mónica C. Quiñones-Frías, Ying Zhang, Avital A. Rodal, Thomas G. Fai
Pages: S476 - S492
Abstract: SIAM Journal on Applied Mathematics, Ahead of Print.
Abstract. The transport of particles in cells is influenced by the properties of intracellular networks they traverse while searching for localized target regions or reaction partners. Moreover, given the rapid turnover in many intracellular structures, it is crucial to understand how temporal changes in the network structure affect diffusive transport. In this work, we use network theory to characterize complex intracellular biological environments across scales. We develop an efficient computational method to compute the mean first passage times for simulating a particle diffusing along two-dimensional planar networks extracted from fluorescence microscopy imaging. We first benchmark this methodology in the context of synthetic networks, and subsequently apply it to live-cell data from endoplasmic reticulum tubular networks.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-11-14T08:00:00Z
DOI: 10.1137/22M1509308
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- Wearable Data Assimilation to Estimate the Circadian Phase
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Authors: Dae Wook Kim, Minki P. Lee, Daniel B. Forger
Pages: S452 - S475
Abstract: SIAM Journal on Applied Mathematics, Ahead of Print.
Abstract. The circadian clock is an internal timer that coordinates the daily rhythms of behavior and physiology, including sleep and hormone secretion. Accurately tracking the state of the circadian clock, or circadian phase, holds immense potential for precision medicine. Wearable devices present an opportunity to estimate the circadian phase in the real world, as they can noninvasively monitor various physiological outputs influenced by the circadian clock. However, accurately estimating circadian phase from wearable data remains challenging, primarily due to the lack of methods that integrate minute-by-minute wearable data with prior knowledge of the circadian phase. To address this issue, we propose a framework that integrates multitime scale physiological data and estimates the circadian phase, along with an efficient implementation algorithm based on Bayesian inference and a new state space estimation method called the level set Kalman filter. Our numerical experiments indicate that our approach outperforms previous methods for circadian phase estimation consistently. Furthermore, our method enables us to examine the contribution of noise from different sources to the estimation, which was not feasible with prior methods. We found that internal noise unrelated to external stimuli is a crucial factor in determining estimation results. Last, we developed a user-friendly computational package and applied it to real-world data to demonstrate the potential value of our approach. Our results provide a foundation for systematically understanding the real-world dynamics of the circadian clock.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-11-09T08:00:00Z
DOI: 10.1137/22M1509680
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- A Non-Local Kinetic Model for Cell Migration: A Study of the Interplay
Between Contact Guidance and Steric Hindrance-
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Authors: Martina Conte, Nadia Loy
Pages: S429 - S451
Abstract: SIAM Journal on Applied Mathematics, Ahead of Print.
Abstract. We propose a non-local model for contact guidance and steric hindrance depending on a single external cue, namely the extracellular matrix, that affects in a twofold way the polarization and speed of motion of the cells. We start from a microscopic description of the stochastic processes underlying the cell re-orientation mechanism related to the change of cell speed and direction. Then, we formally derive the corresponding kinetic model that implements exactly the prescribed microscopic dynamics, and, from it, it is possible to deduce the macroscopic limit in the appropriate regime. Moreover, we test our model in several scenarios. In particular, we numerically investigate the minimal microscopic mechanisms that are necessary to reproduce cell dynamics by comparing the outcomes of our model with some experimental results related to breast cancer cell migration. This allows us to validate the proposed modeling approach and to highlight its capability of predicting qualitative cell behaviors in diverse heterogeneous microenvironments.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-10-24T07:00:00Z
DOI: 10.1137/22M1506389
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- Resource-Driven Pattern Formation in Consumer-Resource Systems with
Asymmetric Dispersal on a Plane-
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Authors: Weiting Song, Shikun Wang, Yuanshi Wang, Donald DeAngelis
Pages: S412 - S428
Abstract: SIAM Journal on Applied Mathematics, Ahead of Print.
Abstract. This paper considers resource-driven pattern formation in consumer-resource systems. Here, a planar pattern consists of many big patches, and a big patch can be regarded as combination of many patches on the plane. The consumer moves between patches asymmetrically, while the asymmetry is driven by the resource abundance. Based on experimental models with linearly-linked patches, we propose a planarly-linked-patch model with asymmetric dispersal. Using dynamical systems theory, we show global stability of equilibria in the model, and demonstrate how the resource-driven dispersal forms patterns. It is shown that appropriate asymmetry in dispersal would make the consumer persist in the system, even in sink patches. The asymmetry could also make the consumer’s total population abundance larger than that without dispersal. However, inappropriate asymmetry would make the consumer go into extinction, even in source patches. Dispersal rates are also shown to play a role in the persistence and abundance increase. Our results are consistent with experimental observations and provide new insights. Numerical simulations by the model reproduce various vegetation patterns in the real world. This work has potential applications in spatial pattern formation in biological research.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-10-19T07:00:00Z
DOI: 10.1137/22M1506006
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- Applications of Mathematical Programming to Genetic Biocontrol
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Authors: Váleri N. Vásquez, John M. Marshall
Pages: S392 - S411
Abstract: SIAM Journal on Applied Mathematics, Ahead of Print.
Abstract. We review existing approaches to optimizing the deployment of genetic biocontrol technologies—tools used to prevent vector-borne diseases such as malaria and dengue—and formulate a mathematical program that enables the incorporation of crucial ecological and logistical details. The model is comprised of equality constraints grounded in discretized dynamic population equations, inequality constraints representative of operational limitations including resource restrictions, and an objective function that jointly minimizes the count of competent mosquito vectors and the number of transgenic organisms released to mitigate them over a specified time period. We explore how nonlinear programming (NLP) and mixed integer nonlinear programming (MINLP) can advance the state of the art in designing the operational implementation of three distinct transgenic public health interventions, two of which are presently in active use around the world.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-09-20T07:00:00Z
DOI: 10.1137/22M1509862
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- Modelling Oxygenic Photogranules: Microbial Ecology and Process
Performance-
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Authors: Alberto Tenore, Maria Rosaria Mattei, Luigi Frunzo
Pages: S362 - S391
Abstract: SIAM Journal on Applied Mathematics, Ahead of Print.
Abstract. This work addresses the modelling of oxygenic photogranules (OPGs), by introducing a mathematical model which describes both the genesis and growth of photogranules and the related treatment process. The photogranule has been modelled as a free boundary domain with radial symmetry, which evolves over time as a result of microbial growth, attachment, and detachment processes. Hyperbolic and parabolic PDEs have been considered to model at mesoscale the transport and growth of sessile biomass and the diffusion and conversion of soluble substrates. The macroscale behavior of the system has been modelled through first order impulsive ordinary differential equations (IDEs), which reproduce a sequencing batch reactor (SBR) configuration. Phototrophic biomass has been considered for the first time in granular biofilms, and cyanobacteria and microalgae have been accounted separately, to model their metabolic differences. To describe the key role of cyanobacteria in the photogranulation process, the attachment velocity of all suspended microbial species has been modelled as a function of the cyanobacteria concentration in suspended form. The model takes into account the main biological processes involved in OPG-based systems: metabolic activity of cyanobacteria, microalgae, heterotrophic and nitrifying bacteria, microbial decay, extracellular polymeric substances (EPS) secretion, symbiotic and competitive interactions between different species, light-dark cycle, light attenuation across the granule, and photoinhibition phenomena. The model has been integrated numerically, and the results show its consistency in describing the photogranule evolution and ecology, and highlight the advantages of the OPG technology, analyzing the effects of the influent wastewater composition and light conditions on the process.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-09-19T07:00:00Z
DOI: 10.1137/22M1483013
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- Discrete Inverse Method for Extracting Disease Transmission Rates from
Accessible Infection Data-
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Authors: Xiunan Wang, Hao Wang
Pages: S336 - S361
Abstract: SIAM Journal on Applied Mathematics, Ahead of Print.
Abstract. Accurate estimation of the transmissibility of an infectious disease is critical to understanding disease transmission dynamics and designing effective control strategies. However, it has always been difficult to estimate the transmission rates due to the unobservability and multiple contributing factors. In this paper, we develop a data-driven inverse method based on discretizations of compartmental differential equation models for estimating time-varying transmission rates of infectious diseases. By developing iteration algorithms for three typical classes of infectious diseases, namely, a disease with seasonal cycles, a disease with nonseasonal cycles, and a disease with no obvious periodicity, we demonstrate that the discrete inverse method is a valuable tool for extracting information from available pandemic or epidemic incidence data. We also obtain insights for some epidemiological phenomena and issues of concern based on each application. Our method is highly intuitive and generates rapid implementation even with multiple years of data instances. In particular, it can be used in conjunction with other data-driven technologies, such as machine learning, to forecast future disease dynamics based on future weather conditions, policy decisions, or human mobility trends, providing guidance to public health authorities.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-08-17T07:00:00Z
DOI: 10.1137/22M1498796
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- Path Integration and the Structural Sensitivity Problem in Partially
Specified Biological Models-
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Authors: Lourdes Juan, Jackson Kulik, Katharine R. Long, Andrew Y. Morozov, Jacob Slocum
Pages: S316 - S335
Abstract: SIAM Journal on Applied Mathematics, Ahead of Print.
Abstract. Biological systems are known to be inherently uncertain and complex, and it is often difficult to justify rigorously functional forms used in a mathematical model. Generally, one chooses some simple function having qualitatively correct behavior without concern for the precise choice of function; the assumption has been that qualitatively similar functions will produce qualitatively similar behavior from the model. However, it has been shown that, in some cases, the qualitative predictions from a model are sensitive to the particular functional form used; this property is known as structural sensitivity. A promising tool for quantification of structural sensitivity is the use of partially specified models, in which some number of functions in equations are not defined explicitly. However, in this approach we cannot rely on the traditional parameter-based framework, where all functional forms are well defined but contain parameters to be determined. The main difficulties are that, mathematically, we need to deal with an infinite-dimensional function space and that a well-defined measure on that space is needed. We propose a novel framework to reveal the structural sensitivity and quantify uncertainty in partially specified biological models based on ordinary differential equations backed up by empirical data. Our method uses path integration, previously introduced in theoretical physics. As an insightful example, we explore structural sensitivity of a well-known tritrophic food chain model in which the functional response of the predator is uncertain, using available experimental data on protozoan predation on bacteria. For the mentioned model, we compare the novel framework with the classical methods of parameter-based sensitivity analysis and demonstrate distinct outcomes for the two approaches. Finally, we discuss a further extension of the proposed framework.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-07-27T07:00:00Z
DOI: 10.1137/22M1499029
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- Nonparametric Inference for the Reproductive Rate in Generalized
Compartmental Models-
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Authors: Imelda Trejo, Yen Ting Lin, Amanda Patrick, Nicolas Hengartner
Pages: S297 - S315
Abstract: SIAM Journal on Applied Mathematics, Ahead of Print.
Abstract. We develop a tractable nonparametric model for the time-varying reproductive rate of infectious diseases that combines the structure of a deterministic compartmental model and a stochastic model for incidence data. We use Bayesian inference to estimate, with uncertainty, the reproductive rate of the Coronavirus 2019 outbreak in the U.S. states of California, Florida, Michigan, New Mexico, New York, and Texas from January 2020 to March 2022. Employing the inferred reproductive rates, we estimate the posterior distribution of the time-varying reproduction numbers for each state. Compering the time-varying reproduction numbers across the states, we identify some epidemic waves, potentially driven from changes in human behavior and virus mutations.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-07-25T07:00:00Z
DOI: 10.1137/22M1505499
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- Extreme Diffusion with Point-Sink Killing Fields: Application to Fast
Calcium Signaling at Synapses-
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Authors: Suney Toste, David Holcman
Pages: S269 - S296
Abstract: SIAM Journal on Applied Mathematics, Ahead of Print.
Abstract. The extreme narrow escape theory describes the statistical properties of the fastest among many identical stochastic particles to escape from a narrow window. We study here the escape time of the fastest particle when a killing term is added inside a one-dimensional interval. Killing represents a degradation that leads to removal of the moving particles with a given probability. Using the time dependent flux for the solution of the diffusion equation, we compute asymptotically the mean time for the fastest to escape alive. We use the present theory to study the role of several killing distributions on the mean extreme escape time for the fastest and compare the results with Brownian simulations. Finally, we discuss some applications to calcium dynamics in neuronal cells.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-07-21T07:00:00Z
DOI: 10.1137/22M1476319
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- Optimal Epidemic Control by Social Distancing and Vaccination of an
Infection Structured by Time Since Infection: The COVID-19 Case Study-
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Authors: Alberto d’Onofrio, Mimmo Iannelli, Piero Manfredi, Gabriela Marinoschi
Pages: S199 - S224
Abstract: SIAM Journal on Applied Mathematics, Ahead of Print.
Abstract. Motivated by the issue of COVID-19 mitigation, in this work we tackle the general problem of optimally controlling an epidemic outbreak of a communicable disease structured by age since exposure, with the aid of two types of control instruments, namely social distancing and vaccination by a vaccine at least partly effective in protecting from infection. By our analyses we could prove the existence of (at least) one optimal control pair. We derived first-order necessary conditions for optimality and proved some useful properties of such optimal solutions. Our general model can be specialized to include a number of subcases relevant for epidemics like COVID-19, such as, e.g., the arrival of vaccines in a second stage of the epidemic, and vaccine rationing, making social distancing the only optimizable instrument. A worked example provides a number of further insights on the relationships between key control and epidemic parameters.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-07-19T07:00:00Z
DOI: 10.1137/22M1499406
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- Spatial Dynamics with Heterogeneity
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Authors: Denis D. Patterson, A. Carla Staver, Simon A. Levin, Jonathan D. Touboul
Pages: S225 - S248
Abstract: SIAM Journal on Applied Mathematics, Ahead of Print.
Abstract. Spatial systems with heterogeneities are ubiquitous in nature, from precipitation, temperature, and soil gradients controlling vegetation growth to morphogen gradients controlling gene expression in embryos. Such systems, generally described by nonlinear dynamical systems, often display complex parameter dependence and exhibit bifurcations. The dynamics of heterogeneous spatially extended systems passing through bifurcations are still relatively poorly understood, yet recent theoretical studies and experimental data highlight the resulting complex behaviors and their relevance to real-world applications. We explore the consequences of spatial heterogeneities passing through bifurcations via two examples strongly motivated by applications. These model systems illustrate that studying heterogeneity-induced behaviors in spatial systems is crucial for a better understanding of ecological transitions and functional organization in brain development.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-07-19T07:00:00Z
DOI: 10.1137/22M1509850
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- Critical Patch Size of a Two-Population Reaction Diffusion Model
Describing Brain Tumor Growth-
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Authors: Duane C. Harris, Changhan He, Mark C. Preul, Eric J. Kostelich, Yang Kuang
Pages: S249 - S268
Abstract: SIAM Journal on Applied Mathematics, Ahead of Print.
Abstract. The critical patch (KISS) size is the minimum habitat size needed for a population to survive in a region. Habitats larger than the critical patch size allow a population to persist, while smaller habitats lead to extinction. We perform a rigorous derivation of the critical patch size associated with a 2-population glioblastoma multiforme (GBM) model that divides the tumor cells into proliferating and quiescent/necrotic populations. We determine that the critical patch size of our model is consistent with that of the Fisher–Kolmogorov–Petrovsky–Piskunov equation, one of the first reaction-diffusion models proposed for GBM, and does not depend on parameters pertaining to the quiescent/necrotic population. The critical patch size may indicate that GBM tumors have a minimum size depending on the location in the brain. We also derive a theoretical relationship between the size of a GBM tumor at steady-state and its maximum cell density, which has potential applications for patient-specific parameter estimation based on magnetic resonance imaging data. Finally, we identify a positively invariant region for our model, which guarantees that solutions remain positive and bounded from above for all time.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-07-19T07:00:00Z
DOI: 10.1137/22M1509631
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- The Role of Clearance in Neurodegenerative Diseases
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Authors: Georgia S. Brennan, Travis B. Thompson, Hadrien Oliveri, Marie E. Rognes, Alain Goriely
Pages: S172 - S198
Abstract: SIAM Journal on Applied Mathematics, Ahead of Print.
Abstract. Alzheimer’s disease, the most common form of dementia, is a systemic neurological disorder associated with the formation of toxic, pathological aggregates of proteins within the brain that lead to severe cognitive decline, and eventually, death. In normal physiological conditions, the brain rids itself of toxic proteins using various clearance mechanisms. The efficacy of brain clearance can be adversely affected by the presence of toxic proteins and is also known to decline with age. Motivated by recent findings, such as the connection between brain cerebrospinal fluid clearance and sleep, we propose a mathematical model coupling the progression of toxic proteins over the brain’s structural network and protein clearance. The model is used to study the interplay between clearance in the brain, toxic seeding, brain network connectivity, aging, and progression in neurodegenerative diseases such as Alzheimer’s disease. Our findings provide a theoretical framework for the growing body of medical research showing that clearance plays an important role in the etiology, progression, and treatment of Alzheimer’s disease.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-07-17T07:00:00Z
DOI: 10.1137/22M1487801
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- Mechanisms for Producing Oscillatory Plane Waves in Discrete and Continuum
Models-
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Authors: Andrea J. Welsh, Bard Ermentrout
Pages: S151 - S171
Abstract: SIAM Journal on Applied Mathematics, Ahead of Print.
Abstract. Plane waves have commonly been observed in recordings of human brains. These waves take the form of spatial phase gradients in the oscillatory potentials picked up by implanted electrodes. We first show that long but finite chains of nearest-neighbor coupled phase oscillators can produce an almost constant phase gradient when the edge effects interact with small heterogeneities in the local frequency. Next, we introduce a continuum model with nonlocal coupling and use singular perturbation methods to show similar interactions between the boundaries and small frequency differences. Finally, we show that networks of Wilson–Cowan equations can generate plane waves with the same mechanism.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-07-13T07:00:00Z
DOI: 10.1137/22M1506523
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- Algebraic Study of Receptor-Ligand Systems: A Dose-Response Analysis
Open Access Article-
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Authors: Léa Sta, Michael F. Adamer, Carmen Molina-París
Pages: S105 - S150
Abstract: SIAM Journal on Applied Mathematics, Ahead of Print.
Abstract. The study of a receptor-ligand system generally relies on the analysis of its dose-response (or concentration-effect) curve, which quantifies the relation between ligand concentration and the biological effect (or cellular response) induced when binding its specific cell surface receptor. Mathematical models of receptor-ligand systems have been developed to compute a dose-response curve under the assumption that the biological effect is proportional to the number of ligand-bound receptors. Given a dose-response curve, two quantities (or metrics) have been defined to characterize the properties of the ligand-receptor system under consideration: amplitude and potency (or half-maximal effective concentration, and denoted by EC[math]). Both the amplitude and the EC[math] are key quantities commonly used in pharmaco-dynamic modeling, yet a comprehensive mathematical investigation of the behavior of these two metrics is still outstanding; for a large (and important) family of receptors, called cytokine receptors, we still do not know how amplitude and EC[math] depend on receptor copy numbers. Here we make use of algebraic approaches (Gröbner basis) to study these metrics for a large class of receptor-ligand models, with a focus on cytokine receptors. In particular, we introduce a method, making use of two motivating examples based on the interleukin-7 (IL-7) receptor, to compute analytic expressions for the amplitude and the EC[math]. We then extend the method to a wider class of receptor-ligand systems, sequential receptor-ligand systems with extrinsic kinase, and provide some examples. The algebraic methods developed in this paper not only reduce computational costs and numerical errors, but allow us to explicitly identify key molecular parameters and rates which determine the behavior of the dose-response curve. Thus, the proposed methods provide a novel and useful approach to perform model validation, assay design and parameter exploration of receptor-ligand systems.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-07-12T07:00:00Z
DOI: 10.1137/22M1506262
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- Analyzing and Mimicking the Optimized Flight Physics of Soaring Birds: A
Differential Geometric Control and Extremum Seeking System Approach with
Real Time Implementation-
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Authors: Sameh A. Eisa, Sameer Pokhrel
Pages: S82 - S104
Abstract: SIAM Journal on Applied Mathematics, Ahead of Print.
Abstract. The mystery of soaring birds, such as albatrosses and eagles, has intrigued biologists, physicists, aeronautical/control engineers, and applied mathematicians for centuries. These fascinating avian organisms are able to fly for long durations while expending little to no energy, utilizing wind to gain lift. This flight technique/maneuver is called dynamic soaring (DS). For biologists and physicists, the DS phenomenon is nothing but a wonder of the very elegant ability of these birds to interact with nature and use its physical ether in an optimal way for better survival and energy efficiency. For the engineering community, the DS phenomenon is a source of inspiration and an unequivocal opportunity for biomimicking. Mathematical characterization of the DS phenomenon in the literature has been limited to optimal control configurations that utilized developments in numerical optimization algorithms along with control methods to identify the optimal DS trajectory taken (or to be taken) by the bird/mimicking system. Unfortunately, all of these methods are highly complex and non-real-time. Hence, the mathematical characterization of the DS problem, we believe, appears to be at odds with the phenomenon/birds-behavior. In this paper, we provide a novel two-layered mathematical approach to characterize, model, mimic, and control DS in a simple real-time implementation, which we believe more effectively decodes the biological behavior of soaring birds. First, we present a differential geometric control formulation and analysis of the DS problem, which allow us to introduce a control system that is simple yet controllable. Second, we establish a link between the DS philosophy and a class of dynamical control systems known as extremum seeking systems. This linkage provides the control input that makes DS a real-time reality. We believe our framework accurately describes the biological behavior of soaring birds and opens the door for geometric control theory and extremum seeking systems to be utilized in biological systems and natural phenomena. Simulation results are provided along with comparisons to powerful optimal control solvers, illustrating the advantages of the introduced method.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-06-26T07:00:00Z
DOI: 10.1137/22M1505566
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- A Gaussian Process Model for Insulin Secretion Reconstruction with
Uncertainty Quantification: Applications in Cystic Fibrosis-
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Authors: Justin Garrish, Christine Chan, Douglas Nychka, Cecilia Diniz Behn
Pages: S65 - S81
Abstract: SIAM Journal on Applied Mathematics, Ahead of Print.
Abstract. Investigation of biological systems often requires reconstruction of an unobservable continuous process from discrete time-series data sampled from a related process or processes. When the reconstructed process cannot be validated with experimental data, it is particularly important to quantify the uncertainty on the inferred process, and new methodologies are needed to support both the inference and uncertainty quantification. This work derives a novel statistical model that combines an established differential model of intra- and extravascular C-peptide dynamics with a Gaussian process model of insulin secretion rate (ISR) in order to provide clinical measures of beta-cell function with quantified uncertainty. These measures are computed from the ISR that is inferred from measured C-peptide data. The model is first validated using synthetic data, and then applied to oral glucose tolerance test (OGTT) data from youth participants with and without cystic fibrosis (CF). Because CF is characterized by scarring and fibrosis of the pancreas, impairment of beta-cell function, rather than reduced insulin sensitivity, is implicated in the early etiology of CF-related diabetes (CFRD). ISR-derived measures of beta-cell function show worsening beta-cell function from healthy control to CF to CFRD groups consistent with previous reports on dysglycemia in CF. However, the model additionally allows uncertainty in the data to be propagated to ISR and ISR-derived measures of beta-cell function. These results provide insight into uncertainty in ISR-derived measures of beta cell function, characterize interindividual variability in CFRD etiology, and provide novel metrics to quantify the pathogenesis of CFRD.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-04-28T08:09:30Z
DOI: 10.1137/22M1506225
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- A Local Continuum Model of Cell-Cell Adhesion
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Authors: C. Falcó, R. E. Baker, J. A. Carrillo
Pages: S17 - S42
Abstract: SIAM Journal on Applied Mathematics, Ahead of Print.
Abstract. Cell-cell adhesion is one the most fundamental mechanisms regulating collective cell migration during tissue development, homeostasis, and repair, allowing cell populations to self-organize and eventually form and maintain complex tissue shapes. Cells interact with each other via the formation of protrusions or filopodia and they adhere to other cells through binding of cell surface proteins. The resulting adhesive forces are then related to cell size and shape and, often, continuum models represent them by nonlocal attractive interactions. In this paper, we present a new continuum model of cell-cell adhesion which can be derived from a general nonlocal model in the limit of short-range interactions. This new model is local, resembling a system of thin-film type equations, with the various model parameters playing the role of surface tensions between different cell populations. Numerical simulations in one and two dimensions reveal that the local model maintains the diversity of cell sorting patterns observed both in experiments and in previously used nonlocal models. In addition, it also has the advantage of having explicit stationary solutions, which provides a direct link between the model parameters and the differential adhesion hypothesis.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-04-27T07:00:00Z
DOI: 10.1137/22M1506079
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- Dynamical Behavior of a Colony Migration System: Do Colony Size and Quorum
Threshold Affect Collective Decision'-
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Authors: Lisha Wang, Zhipeng Qiu, Takao Sasaki, Yun Kang
Pages: S43 - S64
Abstract: SIAM Journal on Applied Mathematics, Ahead of Print.
Abstract. Social insects are ecologically and evolutionarily the most successful organisms on earth and can achieve robust collective behaviors through local interactions among group members. Colony migration has been considered as a leading example of collective decision making in social insects. In this paper, a piecewise colony migration system with recruitment switching is proposed to explore underlying mechanisms and synergistic effects of colony size and quorum on the outcomes of collective decision. The dynamical behavior of the nonsmooth system is studied, and sufficient conditions for the existence and stability of equilibrium are provided. The theoretical results suggest that large colonies are more likely to emigrate to a new site. More interesting findings include but are not limited to that (a) the system may exhibit oscillation when the colony size is below a critical level and (b) the system may also exhibit a bistable state, i.e., the colony migrates to a new site or the old nest depending on the initial size of recruiters. Bifurcation analysis shows that the variations of colony size and quorum threshold greatly impact the dynamics. The results suggest that it is important to distinguish between two populations of recruiters in modeling. This work may provide important insights on how simple and local interactions achieve the collective migrating activity in social insects.
Citation: SIAM Journal on Applied Mathematics
PubDate: 2023-04-27T07:00:00Z
DOI: 10.1137/22M1478690
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