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Rabies is one of the oldest viral diseases and it has been present on every continent except Antarctica. Within the U.S. human rabies cases are quite rare. In the eastern USA, raccoons are the main reservoir hosts and pet vaccination serves as an important barrier against human rabies exposure. In this paper, we develop a compartmental model for rabies transmission amongst raccoons and domestic pets. We find the disease-free equilibria, reproduction numbers for the raccoons and domestic pets. We also determine the vaccination coverage/rates, both for raccoons and pets, needed to achieve the elimination of rabies. [ABSTRACT FROM AUTHOR]

The goal of this paper is to present an analytical solution, by means of the method of manufactured solutions (MMS), for the mathematical model that describes the behaviour of the grain mass aeration process, proposed by Thorpe. In contrast to related papers in the literature, several numerical approximations to solve the mathematical model were used. The finite difference method (FDM), employing the spatial approximations given by the methods of Roberts and Weiss, Leith, upwind difference scheme (UDS), central difference scheme (CDS) and UDS with deferred correction (UDS-C), combined with the explicit, implicit and Crank-Nicolson temporal formulations was applied. The effective order of the discretisation error achieved with the refinement of the mesh was verified by performing an error analysis for all approximations used. In addition, the results obtained numerically were compared to the analytical solution and the CPU (central processing unit) times at different levels of refinement. The difference in the CPU time using the methods CDS - Crank-Nicolson, Roberts and Weiss, and Leith, was very small compared to the method widely used in literature, the UDS - Explicit. It was also verified that the errors obtained by the proposed methods were considerably smaller than the error obtained by the UDS - Explicit method. In light of the above, the Leith method is recommended to numerically solve the grain mass aeration model proposed by Thorpe. • An analytical solution for a model that describes the aeration process was proposed. • Various numerical approximations to solve the model were studied. • Artificial viscosity was used to control oscillations in the studied model. • An error analysis on the numerical solution of the studied model was performed. [ABSTRACT FROM AUTHOR]

The rapid expansion of cities in developing countries has led to many environmental problems, and the mechanism of urban expansion (UE), as a more complex human-land coupled system, has always been a difficult issue to research. This paper introduces a new approach by establishing an analytical framework for spatiotemporal pattern mining, exemplified by studying the urban growth of Changsha City from 1990 to 2019. Initially, an emerging hotspot analysis model (EHA) is employed to examine the spatiotemporal changes of urban growth on a macro scale. Mathematical models are subsequently utilized to quantify the correlations between urban expansion and selected infrastructural and topographical factors. Building on these findings, the paper constructs mathematical models to further quantify the spatiotemporal evolution of various urban sprawl patterns across different regions, aiming to elucidate and quantify the significant variations in UE over time and space. The study reveals that, as an emerging city, Changsha's hotspots of urban expansion prior to 2003 were primarily concentrated in the city centre, subsequently spreading to the periphery. The radial influence of metro stations on UE is notably less than that of railway stations—approximately 3 km versus 8 km—and the impact diminishes rapidly before gradually tapering off. Moreover, UE in Changsha predominantly occurs on slopes with gradients ranging from 1.1° to 7.5°, and significant development capacity is observed at elevations between 36.1 m and 78.3 m above sea level, with a tendency for urban sprawl to migrate to lower elevations. The paper also identifies three distinct patterns of urban expansion across different regions: an initial slow-growth phase, followed by a rapid escalation to a peak, and subsequently a swift decline to near stagnation. Additionally, it highlights a significant correlation between the proportion of built-up areas at the micro-regional scale and the stages of UE. This correlation was quantitatively analysed by constructing a logistic function, which demonstrated a robust fit that effectively captures spatiotemporal heterogeneity in the dynamics of UE. These insights enhance the selection of drivers in urban simulation models and deepen the understanding of the complex dynamics that influence urban development. • New applications of spatiotemporal pattern mining and emerging hotspot analysis in urban expansion. • Exploring the impact of key infrastructure and topographical factors on urban expansion. • Focusing on revealing and quantifying the different inherent expansion mechanisms within various micro scales of cities. • The saturation of built-up areas in local regions correlates with the stages of urban expansion. [ABSTRACT FROM AUTHOR]

The scattering transform is a multilayered, wavelet-based transform initially introduced as a mathematical model of convolutional neural networks (CNNs) that has played a foundational role in our understanding of these networks' stability and invariance properties. In subsequent years, there has been widespread interest in extending the success of CNNs to data sets with non-Euclidean structure, such as graphs and manifolds, leading to the emerging field of geometric deep learning. In order to improve our understanding of the architectures used in this new field, several papers have proposed generalizations of the scattering transform for non-Euclidean data structures such as undirected graphs and compact Riemannian manifolds without boundary. Analogous to the original scattering transform, these works prove that these variants of the scattering transform have desirable stability and invariance properties and aim to improve our understanding of the neural networks used in geometric deep learning. In this paper, we introduce a general, unified model for geometric scattering on measure spaces. Our proposed framework includes previous work on compact Riemannian manifolds without boundary and undirected graphs as special cases but also applies to more general settings such as directed graphs, signed graphs, and manifolds with boundary. We propose a new criterion that identifies to which groups a useful representation should be invariant and show that this criterion is sufficient to guarantee that the scattering transform has desirable stability and invariance properties. Additionally, we consider finite measure spaces that are obtained from randomly sampling an unknown manifold. We propose two methods for constructing a data-driven graph on which the associated graph scattering transform approximates the scattering transform on the underlying manifold. Moreover, we use a diffusion-maps based approach to prove quantitative estimates on the rate of convergence of one of these approximations as the number of sample points tends to infinity. Lastly, we showcase the utility of our method on spherical images, a directed graph stochastic block model, and on high-dimensional single-cell data. [ABSTRACT FROM AUTHOR]

In this paper we study a recently derived mathematical model for nonlinear propagation of waves in the atmosphere, for which we establish the local well-posedness in the setting of classical solutions. This is achieved by formulating the model as a quasilinear parabolic evolution problem in an appropriate functional analytic framework and by using abstract theory for such problems. Moreover, for L 2 -initial data, we construct global weak solutions by employing a two-step approximation strategy based on a Galerkin scheme, where an equivalent formulation of the problem in terms of a new variable is used. Compared to the original model, the latter has the advantage that the L 2 -norm is a Liapunov functional. [ABSTRACT FROM AUTHOR]

In this paper, we study the degenerate parabolic equations of the form u t = a i ′ j ′ u i ′ j ′ + 2 x n 1 + δ 2 a i ′ n u i ′ n + x n 1 + δ a n n u n n + b i ′ u i ′ + x n 1 + δ 2 b n u n + c u + f derived from the Constant Elasticity of Variance model in mathematical finance. Under certain smoothness conditions on coefficients and forcing term, the smoothness of solution for these problems is proved. Since the solution cannot be considered smooth with standard differentiability, we introduced a suitable weighted norm that makes the solution smooth. Using the weighted norm, we define the weighted Hölder space C s k , 2 + α and establish Schauder theory for C s k , 2 + α regularity. [ABSTRACT FROM AUTHOR]

• In this paper, we propose a distorted pulse detection method based on odd function for pulse decomposition, to solve the problem of optical path mismatch in UWFBG array. • In theory, we build a mathematical model of the distortion pulse and derive the corresponding odd function. • Then, we analyze the peak trajectory obtained by the difference curve by simulation, and determine the optimal interference position of the distorted pulse. • Finally, we use the vibrating liquid column method to carry out underwater acoustic sensing experiments, under different conditions of optical path mismatch. • The results show that, when the distance between adjacent UWFBGs is 50 m and pulse width with 100 ns, the gain of harmonic SNR and average PSD is improved from 2.3 dB and 1.8 dB to 11.2 dB and 10.0 dB respectively, under different circumstances with length difference for 1 m, 1.5 m, and 2 m respectively. In this paper, we propose a distorted pulse detection method based on odd function for pulse decomposition, to solve the problem of optical path mismatch in UWFBG array. In theory, we build a mathematical model of the distortion pulse and derive the corresponding odd function. Then, we analyze the peak trajectory obtained by the difference curve by simulation, and determine the optimal interference position of the distorted pulse. Finally, we use the vibrating liquid column method to carry out underwater acoustic sensing experiments, under different conditions of optical path mismatch. The results show that, when the distance between adjacent UWFBGs is 50 m and pulse width with 100 ns, the gain of harmonic SNR and average PSD is improved from 2.3 dB and 1.8 dB to 11.2 dB and 10.0 dB respectively, under different circumstances with length difference for 1 m, 1.5 m, and 2 m respectively. So, the algorithm is more robust to length mismatch, and verifies the effectiveness of the algorithm, and has potential significance for reducing the difficulty of designing the UWFBG array interferometer. [ABSTRACT FROM AUTHOR]

This paper presents a numerical method for modelling cell migration and aggregation due to chemotaxis where the cell is attracted towards the direction in which the concentration of a chemical signal is increasing. In the model presented here, each cell is represented by a system of springs connected together at node points on the cell's membrane and on the boundary of the cell's nucleus. The nodes located on a cell's membrane are subject to a force which is proportional to the gradient of the concentration of the chemical signal which mimics the behaviour of the chemical receptors in the cell's membrane. In particular, the model developed here will consider what happens when two (or more) cells collide and how their membranes connect to each other to form clusters of cells. The methods described in this paper will be illustrated with a number of typical examples simulating cells moving in response to a chemical signal and how they combine to form clusters. • Motion of cells in response to a diffusing chemical signal. • Cells emitting the chemical signal rather that it being in the environment. • Formation of clusters after the cells have collided. • Numerical examples which simulate the behaviour of real cells. [ABSTRACT FROM AUTHOR]

In this paper we analyze the dynamical behavior of a mosquito population with diapausing stages through a mathematical model derived from the classical McKendrick-von Forester equations. The absence of monotonicity properties and the structure of the equations are noticeable features that hinder the use of commonly applied tools in the field. Our main contribution is to provide a novel methodology to derive criteria of global attractivity of a positive solution for periodic and discontinuous delay differential equations. From an applied perspective, we simulate the evolution of Aedes aegypti with diapausing stages. Moreover, we discuss the influence of the diapause parameters on the creation/suppression of population oscillations. [ABSTRACT FROM AUTHOR]

Establishing multi-component phase field models on dynamic surfaces, and exploring the similarities and differences in phase field evolution between evolving and static surfaces, are interesting studies in multi-phase flow problems. This paper focuses on mathematical modeling and numerical simulation of the N-component Cahn-Hilliard model on evolving surfaces. In the modeling process, the evolution of the energy functional, componential mass conservation, and point-wise mass conservation (hyperplane link condition) are considered. On an evolving surface, the energy dissipation law does not hold because the surface velocity can be viewed as an external force in the system. Meanwhile, due to the velocity, the surface area may change, the componential mass conservation property and the hyperplane link condition can not be satisfied simultaneously. From the point of view of preserving these two physical properties of mass conservation, three types of N-component Cahn-Hilliard model are established on the evolving surface: componential mass conservation, point-wise mass conservation, and both componential and point-wise mass conservation. For the numerical simulation, the evolving surface finite element method is considered for the space-time discretization of the proposed model. In order to obtain a linear, decoupled, high-accurate, and stable scheme for long time numerical simulations, the stabilized semi-implicit method is integrated into the framework of the evolving surface finite element method. Through several numerical examples, the rationality of the model and the efficiency of the numerical method are shown. Additionally, three- and four-component phase separation phenomena are shown to investigate the N-component Cahn-Hilliard dynamic on various evolving surfaces. • Mathematical modeling of the N-component Cahn-Hilliard model on evolving surfaces. • The componential and point-wise mass conservation and their discrete preservations on evolving surfaces. • The stabilized semi-implicit method is integrated into the framework of the evolving surface finite element method. • Investigation on the similarities and differences in phase field evolution between evolving and static surfaces. [ABSTRACT FROM AUTHOR]

• A mathematical model is presented for the mesh analysis within gear-shaft-bearing systems. • The coupling relationship and interaction between bearings and gear pairs in gearbox are revealed. • The calculation method for real-time mesh stiffness of gear pairs in complex environment is developed. • The influence mechanism of bearing failures on the mesh characteristics and contact state of gear pairs is explained. • The optimal modification strategy for gear pairs is determined based on the principle of minimum vibration response. To investigate the influence of bearing failures on the mesh characteristics of gear pairs, this paper presents a mathematical model for gear-shaft-bearing systems. Within this simulation method, the model of defective bearings and the contact analysis methodology of gear pairs are integrated into the system equations. Additionally, the coupling mechanism between system components is determined by addressing the misaligned shafts induced by asynchronous bearing vibrations. Furthermore, the torsional deformation of gear teeth generated by uneven load distribution is considered, and a calculation method for mesh stiffness in complex environments is developed. By employing the comprehensive model, the effect of raceway failures on the mesh behavior is lucidly explained, the real-time distribution of contact stress and load on the tooth surface can be obtained, and the optimal modification strategies for gears are formulated. Finally, the proposed model is confirmed through the finite element (FE) model and experimental observation, which provides a potent tool for the performance optimization of gearboxes. [ABSTRACT FROM AUTHOR]

• Mathematical model of "dynamic" asynchronous iterations. • Both the function being iterated and the participants change over time. • Formal definition of what it means for such processes to behave "correctly". • Derives sufficient conditions for correctness. • Formally verified in the proof assistant Agda, library is publicly available. Many problems can be solved by iteration by multiple participants (processors, servers, routers etc.). Previous mathematical models for such asynchronous iterations assume a single function being iterated by a fixed set of participants. We will call such iterations static since the system's configuration does not change. However in several real-world examples, such as inter-domain routing, both the function being iterated and the set of participants change frequently while the system continues to function. In this paper we extend Üresin and Dubois's work on static iterations to develop a model for this class of dynamic or always on asynchronous iterations. We explore what it means for such an iteration to be implemented correctly, and then prove two different conditions on the set of iterated functions that guarantee the full asynchronous iteration satisfies this new definition of correctness. These results have been formalised in Agda and the resulting library is publicly available. [ABSTRACT FROM AUTHOR]

This paper proposes a neural networks-based approach of finding flat output of linearized underactuated mechanical systems (UMS). Given that differential flatness and controllability are equivalent for linear systems, the problem is equivalent to finding the Brunovsky canonical form of linearized UMSs. We use a two degree-of-freedom (2DOF) system to illustrate the theoretical development. The proposed method identifies the local flat output of nonlinear mechanical systems from the measurements only, without a detailed mathematical model. The identification allows us to combine the well-known active disturbance rejection control (ADRC) and differential flatness control. A time-domain direct identification (TDDI) algorithm and its variant based on the algebraic method are proposed for flat output identification (FOID). The neural networks for implementing the TDDI algorithm called FOID-NN are created to evaluate flat output candidates and to use the flat output to reconstruct the system states in terms of a linear mapping. The neural networks are trained with the loss functions defined by reconstruction errors. Two special layers, namely tracking differentiator (TD) and algebraic layer, are inserted in the FOID-NN to handle noisy signal differentiations. Simulations of a cart–pole system and a stable 2DOF nonlinear UMS are carried out to show the range of applications of the FOID-NN. The experimental data of an underactuated rotary crane are used to validate the identified flat output. [ABSTRACT FROM AUTHOR]

Developing surrogate models for costly mathematical models representing physical systems is challenging since it is typically not possible to generate large training data sets, i.e. to create a large experimental design. In such cases, it can be beneficial to constrain the surrogate approximation to adhere to the known physics of the model. This paper presents a novel methodology for the construction of physics-informed polynomial chaos expansions (PCE) that combines the conventional experimental design with additional constraints from the physics of the model represented by a set of differential equations and specified boundary conditions. A computationally efficient means of constructing physically constrained PCEs, termed PC2, are proposed and compared to the standard sparse PCE. Algorithms are presented for both full-order and sparse PC2 expansions and an iterative approach is proposed for addressing nonlinear differential equations. It is shown that the proposed algorithms lead to superior approximation accuracy and do not add significant computational burden over conventional PCE. Although the main purpose of the proposed method lies in combining training data and physical constraints, we show that the PC2 can also be constructed from differential equations and boundary conditions alone without requiring model evaluations. We further show that the constrained PCEs can be easily applied for uncertainty quantification through analytical post-processing of a reduced PCE by conditioning on the deterministic space-time variables. Several deterministic examples of increasing complexity are provided and the proposed method is demonstrated for uncertainty quantification. • PC2 – a novel framework for physically constrained polynomial chaos expansions is proposed. • An efficient algorithm based on constrained least squares and sparse solver is developed. • Analytical uncertainty quantification of approximated PDEs by PC2 is performed. [ABSTRACT FROM AUTHOR]

• A novel model-free finite frequency band H ∞ controller is proposed for turning chatter suppression. • Users can specify frequency band for optimization according to actual requirements. • An iterative algorithm is used without a mathematical model of controlled target. • An off-policy Q -learning method is utilized to minimize manual parameter tuning. Regenerative chatter is an extremely harmful phenomenon in machining, which generally results in overcut and rapid tool wear. This paper presents the design, analysis, and verification of a novel model-free finite frequency band (MFFFB) H ∞ control algorithm, which is dedicated to chatter suppression of turning process. The proposed MFFFB H ∞ controller is established by utilizing the reinforcement Q -learning along with the generalized Kalman-Yakubovich-Popov (GKYP) lemma. Unlike available entire frequency domain (EFD) H ∞ controllers, the proposed approach facilitates a less conservative implementation since the H ∞ performance index is only designed for the concerned frequency band which implies the limited energies of the actuator are mainly focused on this band, and users can specify optimized frequency band according to the actual turning conditions. Furthermore, it permits the construction of H ∞ controller without any knowledge of the dynamic model of turning process, only the data measured from the system state and input are required. Besides, an iterative solution algorithm for H ∞ control on the basis of policy iteration is presented, which decreases the burden on manual parameter adjustment and capable of achieving the optimal solution. Simulation and experiment results demonstrate that the proposed MFFFB H ∞ controller generates significant improvement in chatter-free region compared with EFD H ∞ controller and conventional FFB H ∞ controller. [ABSTRACT FROM AUTHOR]

The paper presents a novel method for predictive modelling of chanterelle mushrooms' drying kinetics. Use of computational techniques and mathematical modelling for chanterelle mushrooms were employed in analysing the drying process using heat pump dryer. Mushrooms were sliced into 20 mm × 20 mm × 30 mm cuboids and 20 mm × Ø40 mm cylinders. Drying air temperatures of 40 °C, 48 °C, and 56 °C were studied. Determination of the best mushrooms' drying process using selected thin layer and computational intelligence models was examined. Drying curves showed a falling rate period while moisture ratio decreased with temperature rise from 40 °C to 56 °C. Mushrooms' moisture diffusivities rose from 23.709 × 10−8 m2s−1 to 41.035 × 10−8 m2s−1 as temperature rose from 40 °C to 56 °C for the cuboid slices. Similarly, diffusivities for cylindrical mushrooms rose from 9.322 × 10−8 m2s−1 to 12.1585 × 10−8 m2s−1. The activation energy of cuboidal mushrooms was 29.3908 kJmol-1 while that of cylindrical sample was 14.2856 kJmol-1. Statistical parameters used showed that Midilli et al. was the most superior thin-layer drying model in predicting drying kinetics of chanterelle mushrooms. 1–3 ANN architecture was the best architectures in predicting drying process of chanterelle mushrooms. Standardized Pearson universal kernel was the best SVM filter. A k = 5 value was the best kNN values tested in predicting the chanterelle mushrooms drying process. However, tested data for standardized Pearson universal kernel was the most superior among conventional and intelligent models used. Consequently, computational intelligence modelling especially the standardized Pearson universal kernel was recommendable in modelling drying kinetics of chanterelle mushrooms under heat pump dryer. • Temperature and shape variations influenced the moisture ratio of mushrooms. • D eff ranged from 23.7 × 10−8-41.0 × 10−8 m2s−1 with temperature rise in cuboids. • E a was 29.3908 kJmol-1 and 14.2856 kJmol-1 mushroom cuboids and cylinders. • Midilli et al. thin-layer model gave the lowest minimal moisture ratio variations. • SVM was the best in describing drying process of both shapes chanterelle mushrooms. [ABSTRACT FROM AUTHOR]

The dominant paradigm for modeling the obesity-induced T2DM (type 2 diabetes mellitus) today focuses on glucose and insulin regulatory systems, diabetes pathways, and diagnostic test evaluations. The problem with this approach is that it is not possible to explicitly account for the glucose transport mechanism from the blood to the liver, where the glucose is stored, and from the liver to the blood. This makes it inaccurate, if not incorrect, to properly model the concentration of glucose in the blood in comparison to actual glycated hemoglobin (A1C) test results. In this paper, we develop a mathematical model of glucose dynamics by a system of ODEs. The model includes the mechanism of glucose transport from the blood to the liver, and from the liver to the blood, and explains how obesity is likely to lead to T2DM. We use the model to evaluate the efficacy of an anti-T2DM drug that also reduces weight. [ABSTRACT FROM AUTHOR]

[Display omitted] • The integration of vibration reduction and energy harvesting for space vehicles is studied. • An electromagnetic-pneumatic regenerative shock absorber is proposed for the first time. • The coupling model of friction-electromagnetic-pneumatic damping is established. • The proposed new regenerative shock absorber has excellent damping smoothness. In recent years, the development of space exploration has attracted much attention. In order to save energy for lunar/mars rover, an electromagnetic-pneumatic regenerative shock absorber (EP-RSA) is proposed in this paper, which can harvest the vibration energy of rovers traveling on rough roads. Structurally, the design of the hybrid regenerative shock absorber includes three modules: vibration input, transmission, and generator. It is worth emphasizing that the transmission module involves pneumatic damping to provide enough damping force and improve the driving comfort for the rover. Mathematical modeling and simulation analysis of the dynamics and energy harvesting characteristics of the EP-RSA are carried out. Finally, the system prototype is manufactured and the dynamic and energy output performance are tested in the bench test environment. The experimental results show that the introduction of pneumatic damping makes the force–displacement curve smoother, and the damping force is increased by nearly 50 times. Meanwhile, the power output results of the system match the simulation results, and the average power can reach 1.26 W, indicating that the proposed EP-RSA is promising for the energy saving and dynamics improvement of the space exploration rover. [ABSTRACT FROM AUTHOR]

• I briefly describe the Boolean modeling approach to investigate gene regulatory networks (GRNs). • I discuss the foundational contributions by the three seminal manuscripts more than 15 years ago. • Finally, the applications of the Boolean modeling approach to the large-scale omics data is discussed. Boolean modeling is a mathematical modeling framework used for defining and studying gene-regulatory networks (GRNs). It serves as a means to develop mechanistic models, offering insights into the trajectories and dynamic properties of GRNs. In this review, I delve into seminal papers published in the Journal of Theoretical Biology that have spearheaded this field. Additionally, I explore the application of these modeling methods in the current era of data-intensive science. [ABSTRACT FROM AUTHOR]

Hydrodynamic cavitation has been a promising method and technology in wastewater treatment, while the principles based on the design of cavitational reactors to optimize cavitation yield and performance remains lacking. Computational fluid dynamics (CFD), a supplementation of experimental optimization, has become an essential tool for this issue, owing to the merits of low investment and operating costs. Nevertheless, researchers with a non-engineering background or few CFD fundamentals used straightforward numerical strategies to treat cavitating flows, and this might result in many misinterpretations and consequently poor computations. This review paper presents the rationale behind hydrodynamic cavitation and application of cavitation modeling specific to the reactors in wastewater treatment. In particular, the mathematical models of multiphase flow simulation, including turbulence closures and cavitation models, are comprehensively described, whilst the advantages and shortcomings of each model are also identified and discussed. Examples and methods of the coupling of CFD technology, with experimental observations to investigate into the hydrodynamic behavior of cavitating devices that feature linear and swirling flows, are also critically summarized. Modeling issues, which remain unaddressed, i.e., the implementation strategies of numerical models, and the definition of cavitation numbers are identified and discussed. Finally, the advantages of CFD modeling are discussed and the future of CFD applications in this research area is also outlined. It is expected that the present paper would provide decision-making support for CFD beginners to efficiently perform CFD modeling and promote the advancement of cavitation simulation of reactors in the field of wastewater treatment. • Computational models applied in reactors for wastewater treatment were summarized. • Numerical simulations contribute to the research of cavitational reactors. • Numerical research into rotating cavitational reactors needs advanced strategies. • A new parameter based on the flow is suggested for the study of cavitation yields. [ABSTRACT FROM AUTHOR]

The paper presents a novel methodology to build surrogate models of complicated functions by an active learning-based sequential decomposition of the input random space and construction of localized polynomial chaos expansions, referred to as domain adaptive localized polynomial chaos expansion (DAL-PCE). The approach utilizes sequential decomposition of the input random space into smaller sub-domains approximated by low-order polynomial expansions. This allows the approximation of functions with strong nonlinearities, discontinuities, and/or singularities that often appear in dynamical systems. Decomposition of the input random space and local approximations alleviates the Gibbs phenomenon for these types of problems and confines error to a very small vicinity near the non-linearity. The global behavior of the surrogate model is therefore significantly better than existing methods, as shown in numerical examples, including an engineering dynamical system exhibiting discontinuous response. The whole process is driven by an active learning routine that uses the recently proposed Θ criterion to assess local variance contributions (Novák et al., 2021). The proposed approach balances both exploitation of the surrogate model and exploration of the input random space and thus leads to efficient and accurate approximation of the original mathematical model. The numerical results show the superiority of the DAL-PCE in comparison to (i) a single global polynomial chaos expansion and (ii) the recently proposed stochastic spectral embedding (SSE) method (Marelli et al., 2021) developed as an accurate surrogate model and which is based on a similar domain decomposition process. This method represents a general framework upon which further extensions and refinements can be based and which can be combined with any technique for non-intrusive polynomial chaos expansion construction. • Effective construction of a general approximation based on polynomial chaos expansion. • Novel method for domain decomposition and construction of local approximations. • Sequential domain decomposition and sample size extension based on an active learning. • Active learning represented by variance-based criterion for polynomial chaos expansion. [ABSTRACT FROM AUTHOR]

In this paper, we present a detailed numerical scheme for a single-phase compressible flow without diffusion of a multi-component mixture in porous media with the higher-order approximation in both space and time. The mathematical model consists of Darcy velocity, transport equations for each component of a mixture, pressure equation and associated relations for physical quantities such as viscosity or equation of state. The discrete problem is obtained using a combination of the discontinuous Galerkin method for the transport equations and the mixed-hybrid finite element method for the Darcy velocity and the pressure equation. In both methods the higher-order approximation is used. The resulting nonlinear problem for concentrations is solved with the fully mass-conservative iterative IMPEC method. Experimental order of convergence analysis (EOC) and some numerical experiments of a 2D flow are carried out. • A new numerical scheme is presented for simulation of single-phase flow in a porous medium. • The second-order approximation is attained in both space and time. • The second-order approximation in both time and space is verified using the experimental order of convergence. • Several computational examples illustrate advantageous features of our approach. [ABSTRACT FROM AUTHOR]

The paper presents a novel approach for prototyping and modelling of the Adaptive Tuned Particle Impact Damper (ATPID). After introducing the operation and potential disadvantages of the classical Particles Impact Dampers (PIDs) the authors propose the concept of single-grain controllable damper, which can adapt to actual dynamic excitation by a real-time change of the container height. The investigations focus on the methodology of simplified mathematical modelling of the ATPID damper based on grain physical properties, nonlinear soft contact theory, and control function of the absorber height being a novel component used to optimize dynamic response of the system. The proposed ATPID model is positively verified against the experimental results obtained from the developed test stand including a vibrating beam equipped with the proposed innovative attenuator. The conducted analyses clearly reveal the operating principles of the ATPID damper, the types of grain movement, the influence of shock absorber parameters on the vibrating system response and the energy balance of the system. The solution of the formulated optimization problem aimed at minimization of vibration amplitudes allows to find the optimal damper height for various physical parameters of the grain and the external excitation and to achieve a high efficiency of the proposed damper reaching 90%. In addition, a real-time control strategy providing adaptation of the ATPID damper to changing amplitude of kinematic excitation and effective mitigation of steady-state vibrations is proposed and verified experimentally. • Novel approach for prototyping and modelling of the Adaptive Tuned Particle Impact Damper (ATPID). • Controllable damper, which can adapt to actual dynamic excitation by a real-time change of the container height. • The analyses clearly reveal the operating principles of the ATPID damper. • The optimization process allows to find the optimal damper heights for various parameters. • A real-time control strategy of the ATPID damper and experimental verification is revealed. [ABSTRACT FROM AUTHOR]

We consider the uniaxial growth of a tissue or colony of cells, where a nutrient (or some other chemical) required for cell proliferation is supplied at one end, and is consumed by the cells. An example would be the growth of a cylindrical yeast colony in the experiments described by Vulin et al. (2014). We develop a reaction–diffusion model of this scenario which couples nutrient concentration and cell density on a growing domain. A novel element of our model is that the tissue is assumed to be compressible. We define replicative regions, where cells have sufficient nutrient to proliferate, and quiescent regions, where the nutrient level is insufficient for this to occur. We also define pathlines, which allow us to track individual cell paths within the tissue. We begin our investigation of the model by considering an incompressible tissue where cell density is constant before exploring the solution space of the full compressible model. In a large part of the parameter space, the incompressible and compressible models give qualitatively similar results for both the nutrient concentration and cell pathlines, with the key distinction being the variation in density in the compressible case. In particular, the replicative region is located at the base of the tissue, where nutrient is supplied, and nutrient concentration decreases monotonically with distance from the nutrient source. However, for a highly-compressible tissue with small nutrient consumption rate, we observe a counter-intuitive scenario where the nutrient concentration is not necessarily monotonically decreasing, and there can be two replicative regions. For parameter values given in the paper by Vulin et al. (2014), the incompressible model slightly overestimates the colony length compared to experimental observations; this suggests the colony may be somewhat compressible. Both incompressible and compressible models predict that, for these parameter values, cell proliferation is ultimately confined to a small region close to the colony base. • Reaction–diffusion model of uniaxial growth with coupled nutrient concentration and compressible cell density. • Cell pathlines used to determine regions of uniform and non-uniform proliferation. • Counter-intuitive result found that predicts two replicative regions of cell proliferation. • Model parameterised with yeast data provides good quantitative match with experiments. [ABSTRACT FROM AUTHOR]

In mathematical modelling, the data and solutions are represented as measurable functions and their quality is oftentimes captured by the membership to a certain function space. One of the core questions for an analysis of a model is the mutual relationship between the data and solution quality. The optimality of the obtained results deserves a special focus. It requires a careful choice of families of function spaces balancing between their expressivity, i.e. the ability to capture fine properties of the model, and their accessibility, i.e. its technical difficulty for practical use. This paper presents a unified and general approach to optimality problems in Orlicz spaces. Orlicz spaces are parametrized by a single convex function and neatly balance the expressivity and accessibility. We prove a general principle that yields an easily verifiable necessary and sufficient condition for the existence or the non-existence of an optimal Orlicz space in various tasks. We demonstrate its use in specific problems, including the continuity of Sobolev embeddings and boundedness of integral operators such as the Hardy–Littlewood maximal operator and the Laplace transform. [ABSTRACT FROM AUTHOR]

Signal processing is an important research topic. This paper aims to provide a general framework for signal processing on arbitrary dynamic graphs. We propose a new graph transformation by defining a temporal-attention product. This product transforms the sequence of graph time slices with arbitrary topology and number of nodes into a static graph, effectively capturing graph signals' spatio-temporal dynamic evolution process. The temporal-attention product graph provides a solid mathematical foundation to model the time-dependent graph signal processes as martingales. The weighted adjacency matrix obtained by temporal-attention products is a block tridiagonal matrix, which has been extensively studied. Therefore, it is general and convenient to perform graph signal processing on this new static graph. We apply two real datasets to illustrate the effectiveness of spectral graph wavelet transform based on temporal-attention product. For one of the datasets with no graph structure, we learn the graph weights through a neural network. [ABSTRACT FROM AUTHOR]

• We recall some preliminaries concerning stem cell therapy for cardiac regeneration and related mathematical models. • We write the systems of partial differential equations and the boundary and initial conditions. • We show some numerical results obtained integrating numerically the systems of equations. Stem cell therapy is a promising treatment for the regeneration of myocardial tissue injured by an ischemic event. Mathematical modeling of myocardial regeneration via stem cell therapy is a challenging task, since the mechanisms underlying the processes involved in the treatment are not yet fully understood. Many aspects must be accounted for, such as the spread of stem cells and nutrients, chemoattraction, cell proliferation, stages of cell maturation, differentiation, angiogenesis, stochastic effects, just to name a few. In this paper we propose a 3D mathematical model with a free boundary that aims to provide a qualitative description of some main aspects of the stem cell regenerative therapy in a simplified scenario. The paper mainly focuses on the description of the shrinking of the necrotic core during treatment. The stem cell and nutrients dynamics are described through coupled reaction-diffusion problems. Proliferation, chemoattraction, tissue regeneration and nutrient consumption are included in the model. [ABSTRACT FROM AUTHOR]

• Understanding the theory behind DCM is crucial to avoid pitfalls in its application. • In this review, the equations of conductance-based DCM are derived step-by-step. • Aspects of software implementation are highlighted. • Data are simulated to provide an intuition of the model's capabilities. • The code used is freely available and provided alongside the manuscript. Dynamic Causal Modeling (DCM) is a Bayesian framework for inferring on hidden (latent) neuronal states, based on measurements of brain activity. Since its introduction in 2003 for functional magnetic resonance imaging data, DCM has been extended to electrophysiological data, and several variants have been developed. Their biophysically motivated formulations make these models promising candidates for providing a mechanistic understanding of human brain dynamics, both in health and disease. However, due to their complexity and reliance on concepts from several fields, fully understanding the mathematical and conceptual basis behind certain variants of DCM can be challenging. At the same time, a solid theoretical knowledge of the models is crucial to avoid pitfalls in the application of these models and interpretation of their results. In this paper, we focus on one of the most advanced formulations of DCM, i.e. conductance-based DCM for cross-spectral densities, whose components are described across multiple technical papers. The aim of the present article is to provide an accessible exposition of the mathematical background, together with an illustration of the model's behavior. To this end, we include step-by-step derivations of the model equations, point to important aspects in the software implementation of those models, and use simulations to provide an intuitive understanding of the type of responses that can be generated and the role that specific parameters play in the model. Furthermore, all code utilized for our simulations is made publicly available alongside the manuscript to allow readers an easy hands-on experience with conductance-based DCM. [ABSTRACT FROM AUTHOR]

Membrane-based purification of therapeutic agents has recently attracted global attention as a promising replacement for conventional techniques like distillation and pervaporation. Despite the conduction of different investigations, development of more research about the operational feasibility of using polymeric membranes to separate the detrimental impurities of molecular entities is of great importance. The focus of this paper is to develop a numerical strategy based on multiple machine learning methods to predict the concentration distribution of solute through a membrane-based separation process. Two inputs are being analyzed in this study, specifically r and z. Furthermore, the single target output is C , and the number of data points exceeds 8000. To analyze and model the data for this study, we used the Adaboost (Adaptive Boosting) model over three different base learners (K-Nearest Neighbors (KNN), Linear Regression (LR), and Gaussian Process Regression (GPR)). In the process of hyper-parameter optimization for models, the BA optimization algorithm applied on the adaptive boosted models. Finally, Boosted KNN, Boosted LR, and Boosted GPR have scores of 0.9853, 0.8751, and 0.9793 in terms of R2 metric. Based on the recent fact and other analyses, boosted KNN model is introduced as the most appropriate model of this research. The error rates for this model are 2.073 × 101 and 1.06 × 10−2 in terms of MAE and MAPE metrics. • Predicting concentration distribution of solute through a membrane-based process. • Machine learning model development using CFD data. • Optimization of hyper-parameters using BA algorithm. [ABSTRACT FROM AUTHOR]

The coconut rhinoceros beetle (CRB), is one of the most damaging pests to coconut palms causing severe economic harm. Its expansion from Asia to the Pacific in the early 20th century has been stopped by virus control. However, a new haplotype CRB-Guam has recently escaped this control and invaded Guam, other Pacific islands, and has even established itself in the Western Hemisphere. In this paper, we present a compartmental ODE model of CRB population and control. We carefully consider CRB life stages and its interplay with coconut palms as well as "the green waste", the organic matters used by CRB for breeding sites. We calibrate and validate the model based on data count of CRBs trapped in Guam between 2008 and 2014. We derive the basic reproduction number determining the CRB population growth without any control measures. We also identify control levels required to eliminate CRBs. We show that, in the absence of viable virus control, the sanitation, i.e., the removal of the green waste is the most efficient way to control the population. Our model predicts that the sanitation efforts need to roughly double from the current levels to eliminate CRB from Guam. Furthermore, we demonstrate that a rare event like Typhoon Dolphin that hit Guam in 2015 can lead to a quick rise of the CRB population. • The removal of the green waste is the most efficient control of CRBs. • A typhoon directly hitting Guam can lead to a quick rise of the CRB population. • A decline of the CRB population is not an indication that the invasion is resolved. [ABSTRACT FROM AUTHOR]

• A novel modeling method for convoluted air springs is proposed to estimate the vertical stiffness. • Both the effects of bellow's tensile deformation and the asymmetric structural features are considered in the proposed model. • The proposed model is fully solved and derived to a unified model as a function of the number of bellows. The article presents a novel mathematical model to analyze the performance of convoluted air springs (CAS) with different numbers of bellows. The proposed mathematical model considers both the effects of bellow's tensile deformation and the asymmetric structural features. Some key parameters such as effective area, volume, and their variation rates are derived based on geometric analysis to establish the analytical model of the vertical stiffness and maximum outer diameter. Three types of CAS with single, double, and triple bellows are designed and manufactured for testing the performances. The developed model presented in this paper is compared with another three analytical models based on different assumptions and simplified methods by comparing the estimated stiffness and maximum outer diameter. The comparison demonstrates that the proposed model in this paper has higher accuracy than that of the others and has a uniform formula as a function of the number of bellows to calculate performances of CAS. It is also shown that for the simplified model, ignoring the tensile deformation of the bellows or the asymmetry of the model will introduce large calculation errors for the stiffness up to 10.96%. The reasons for the estimated errors compared with experiment are analyzed at the end of the article. [ABSTRACT FROM AUTHOR]

In this paper, we consider flow and transport problems in thin domains. Modeling problems in thin domains occur in many applications, where thin domains lead to some type of reduced models. A typical example is one dimensional reduced-order model for flows in pipe-like geometries (e.g., blood vessels). In many reduced-order models, the model equations are described apriori by some analytical approaches. In this paper, we propose the use of multiscale methods, which are alternative to reduced-order models and can represent reduced-dimension modeling by using fewer basis functions (e.g., the use of one basis function corresponds to one dimensional approximation). The mathematical model considered in the paper is described by a system of equations for velocity, pressure, and concentration, where the flow is described by the Stokes equations, and the transport is described by an unsteady convection-diffusion equation with non-homogeneous boundary conditions on walls (reactive boundaries). We start with the finite element approximation of the problem on unstructured grids and use it as a reference solution for two and three-dimensional model problems. Fine grid approximation resolves complex geometries on the grid level and leads to a large discrete system of equations that is computationally expensive to solve. To reduce the size of the discrete systems, we develop a multiscale model reduction technique, where we construct local multiscale basis functions to generate a lower-dimensional model on a coarse grid. The proposed multiscale model reduction is based on the Discontinuous Galerkin Generalized Multiscale Finite Element Method (DG-GMsGEM). In DG-GMsFEM for flow problems, we start with constructing the snapshot space for each interface between coarse grid cells to capture possible flows. For the reduction of the snapshot space size, we perform a dimension reduction via a solution of the local spectral problem and use eigenvectors corresponding to the smallest eigenvalues as multiscale basis functions for the approximation on the coarse grid. For the transport problem, we construct multiscale basis functions for each interface between coarse grid cells and present additional basis functions to capture non-homogeneous boundary conditions on walls. Finally, we will present some numerical simulations for three test geometries for two and three-dimensional problems to demonstrate the method's performance. • Design of multiscale methods and concepts for thin domain problems. • Dimension reduction using multiscale methods. • Multiscale methods for problems with irregular boundaries. • Coupled flow and transport problems in thin domains. [ABSTRACT FROM AUTHOR]

Despite years of combined antiretroviral therapy (cART), HIV persists in infected individuals. The virus also rebounds after the cessation of cART. The sources contributing to viral persistence and rebound are not fully understood. When viral rebound occurs, what affects the time to rebound and how to delay the rebound remain unclear. In this paper, we started with the data fitting of an HIV infection model to the viral load data in treated and untreated humanized myeloid-only mice (MoM) in which macrophages serve as the target of HIV infection. By fixing the parameter values for macrophages from the MoM fitting, we fit a mathematical model including the infection of two target cell populations to the viral load data from humanized bone marrow/liver/thymus (BLT) mice, in which both CD4+ T cells and macrophages are the target of HIV infection. Data fitting suggests that the viral load decay in BLT mice under treatment has three phases. The loss of infected CD4+ T cells and macrophages is a major contributor to the first two phases of viral decay, and the last phase may be due to the latent infection of CD4+ T cells. Numerical simulations using parameter estimates from the data fitting show that the pre-ART viral load and the latent reservoir size at treatment cessation can affect viral growth rate and predict the time to viral rebound. Model simulations further reveal that early and prolonged cART can delay the viral rebound after cessation of treatment, which may have implications in the search for functional control of HIV infection. • A macrophage infection model is fit to humanized myeloid-only (MoM) mouse data. • A model with two targets of HIV infection is fit to humanized BLT mouse data. • We studied the viral load decay dynamics in BLT mice under treatment. • We evaluated what might cause a rapid viral rebound after treatment cessation. [ABSTRACT FROM AUTHOR]

In natural language generation, most decoding methods are not intrinsic because their performance depends on extrinsically configured hyperparameters. It means that: first, the generation system is dynamic under different conditions while the decoding system is always static under any conditions once its hyperparameters are extrinsically fixed; second, it is hard to select a constant decoding hyperparameter that is omnipotent for all conditions. Although there are decoding methods that are hyperparameter-free, such as greedy and plain sampling, it has been well studied that these methods generally perform worse than methods with hyperparameters, such as beam search, top-k and top-p. Decoding with hyperparameters can get infinite strategies from different fixed configurations, while hyperparameter-free methods have only one strategy. Therefore, the comparison between them is actually unfair, which is a one-vs-infinite battle. So how to deal with the decoding hyperparameters properly and intrinsically? Is it true that hyperparameter-free methods are always inferior to methods with inexhaustible hyperparameter configurations? Is it possible to design a generalized framework, by which these decoding methods can be naturally connected, uniformly described, and mutually inspired? In these paper, we try to find answers to these questions. To this end, we first propose a generalized decoding framework, i.e., GSD, that can be used to uniformly describe and connect existing popular decoding methods. As far as we know, this is the first work trying to build a theoretical framework to associate these decoding methods in formal mathematical theorems. Based on the framework, we then propose Intrinsic Decoding, a novel implementation of GSD with distinctive design from existing decoding algorithms: it is intrinsic and dynamic. Intrinsic Decoding changes the aforementioned comparison from one-vs-infinite to dynamic-vs-infinite. Just like greedy and sampling, Intrinsic Decoding has no hyperparameter, while effecting better than both greedy and sampling, even achieving comparable performance to the methods equipped with inexhaustible hyperparameter configurations, such as beam search, top-k and top-p. [ABSTRACT FROM AUTHOR]

• A model is proposed based on the key role of Regulatory T cells in chemoimmunotherapy. • The model's fixed points are obtained and the bifurcation diagrams are discussed. • New features of personalizing a cancer mathematical model are presented. • Considering Regulatory T cells leads to identifying critical patient conditions more precisely. Studying the mathematical dynamics of cancer has gained the attention of bioengineers in the past three decades. Different kinds of modelling considering various aspects of treatment have been proposed. In this paper, the key role of Regulatory T cells is discussed and a model in ordinary differential equation (ODE) form is proposed by adding this state to the system dynamics considering chemoimmunotherapy treatment. Regulatory T cells are considered as one of the main tumor cells' tactics to deceive the body's immune system. The improved model is verified mathematically and biologically and fits all criteria in both fields. The results show that entering Regulatory T cells state on cancer mathematical modelling for simulating body cells for chemoimmunotherapy provides a way to identify critical cases more carefully, which a simplified model is unable to accomplish. This point emphasizes the fact that this state must be present in cancer modelling to anticipate immune response more accurately. The advanced system fixed points are obtained by the Newton method and bifurcation diagrams are derived and discussed. New features and remarks are proposed during the journey of developing more accurate models that have the best fit with laboratory data. The sensitivity chart of the model is illustrated and novel aspects of discussions are made with the aim of personalizing a model for a patient and identifying critical conditions based on the chart before any treatment begins. This point enables physicians to determine whether critical conditions have occurred for a patient in a specific treatment or not. [ABSTRACT FROM AUTHOR]

A principal objective in agriculture is to maximise food production; this is particularly relevant with the added demands of an ever increasing population, coupled with the unpredictability that climate change brings. Further improvements in productivity can only be achieved with an increased understanding of plant and crop processes. In this respect, mathematical modelling of plants and crops plays an important role. In this paper we present a two-scale mathematical model of crop yield that accounts for plant growth and canopy interactions. A system of nonlinear ordinary differential equations (ODEs) is formulated to describe the growth of each individual plant, where equations are coupled via a term that describes plant competition via canopy–canopy interactions. A crop of greenhouse plants is then modelled via an agent based modelling approach in which the growth of each plant is described via our system of ODEs. The model is formulated for the African drought tolerant legume bambara groundnut (Vigna subterranea), which is currently being investigated as a food source in light of climate change and food insecurity challenges. Our model allows us to account for plant diversity and also investigate the effect of individual plant traits (e.g. plant canopy size and planting distance) on the yield of the overall crop. Informed with greenhouse data, model results show that plant positioning relative to other plants has a large impact on individual plant yield. Variation in physiological plant traits from genetic diversity and the environmental effects lead to experimentally observed variations in crop yield. These traits include plant height, plant carrying capacity, leaf accumulation rate and canopy spread. Of these traits plant height and ground cover growth rates are found to have the greatest impact on crop yield. We also consider a range of different planting arrangements (uniform grid, staggered grid, circular rings and random allocation) and find that the staggered grid leads to the greatest crop yield (6% more compared to uniform grid). Whilst formulated specifically for bambara groundnut, the generic formulation of our model means that with changes to certain parameter's, it may be extended to other crop species that form a canopy. • Development of a multiscale (plant to crop scale) mathematical model. • The model is formulated for bambara groundnut but easily adapted to other species. • The model describes individual plant physiology and interplant competition. • Various planting arrangements are investigated for the greatest total crop yield. • Considering different genetic traits plant height has the greatest effect on yield. [ABSTRACT FROM AUTHOR]

Rotor dynamic force coefficients of gas seals strongly depend on the machine operational conditions. These force coefficients influence the overall dynamical response and modal properties of machines, consequently defining the machine vibration levels. Accurate estimations of the rotor dynamic coefficients are required for designing machines with low vibration amplifications and well-defined stability margins throughout the operational range. Experimental methods applied to test benches are used to validate such force coefficients and they normally rely on (i) the quality of the measurements and (ii) the assumption that the mathematical model is able to capture the whole system dynamics. If relevant dynamical contributions in a system are neglected by the mathematical model, the contribution will erroneously be concluded to originate from the seal being tested. The theoretical and experimental investigation in this paper focuses on quantifying and qualifying the effect of neglected system dynamics modelling on the estimation of seals force coefficients and stability margins. The in-situ identification of seal forces shows that the direct stiffness, cross-coupling stiffness, and direct damping coefficient estimations for a gas seal with high preswirl are statistically significantly affected by the baseline model. Nevertheless, the baseline model leads to small deviations of the seal force coefficient estimations. The prediction accuracy of stability margins is found to be more influenced by the baseline model describing the system dynamics than by the deviations between the seal force coefficient estimations. [ABSTRACT FROM AUTHOR]

This paper discusses a possibility of using a new type of bifurcation diagrams that can be computed for time series being either solutions of nonlinear oscillatory dynamical systems or measured and recorded in a laboratory when no mathematical model is known. The obtained or measured noisy time-series in mechanical (and in other areas of engineering) dynamical systems are analyzed in a certain range of a slowly varying parameter and the added noise is uncorrelated with the dynamics of the system. In such a scenario with noise, typical well-known bifurcation diagrams cannot be used, so a new method of computing bifurcation diagrams via hypothesis testing from statistics is proposed - a method based on pseudo-periodic surrogates and correlation dimension as the discriminating statistics. An illustrative example based on the chaotic Rössler system is provided to show promising results of this new approach. • Hypothesis testing can be used to compute new bifurcation diagrams. • Correlation dimension serves as a discriminating statistic. • The diagrams differentiate between pseudo-periodic and chaotic time-series. • Computations are based on the pps algorithm combined with a few Matlab functions. [ABSTRACT FROM AUTHOR]

This paper presents a mathematical model capable to reproduce a celebrated phenomenon in blood microcirculation known as Fåhræus effect, since its discovery by Robin Fåhræus (1929). This consists in a decaying of the relative hematocrit in small vessels as the vessel diameter decreases. The key point of the model is a formula, direct consequence of the basic principles of fluid dynamics, that links the relative hematocrit to the reservoir hematocrit and the vessel diameter, which confirms the observed behavior. To test the model we selected, among the few experiments carried on since then, those performed by Barbee and Cokelet (1971). The agreement is remarkable. An extended comparison is also carried out with a celebrated empirical formula proposed by Pries et al. (1992) to describe the same phenomenon. • Modeling of blood flow in medium–large microvessels. • Theoretical description of the Fåhræus effect. • Explicit formulas for H T as a function of H D. • Comparison with the Barbee–Cokelet experiments. [ABSTRACT FROM AUTHOR]

• Coordination of scientific research communities supported mathematical modelling of COVID-19. • Pre-existing research collaborations contributed to the success of coordination initiatives. • National infrastructure is key to support nationwide research networks. • Evidence synthesis important in supporting scientists providing advice to government. In March 2020 mathematics became a key part of the scientific advice to the UK government on the pandemic response to COVID-19. Mathematical and statistical modelling provided critical information on the spread of the virus and the potential impact of different interventions. The unprecedented scale of the challenge led the epidemiological modelling community in the UK to be pushed to its limits. At the same time, mathematical modellers across the country were keen to use their knowledge and skills to support the COVID-19 modelling effort. However, this sudden great interest in epidemiological modelling needed to be coordinated to provide much-needed support, and to limit the burden on epidemiological modellers already very stretched for time. In this paper we describe three initiatives set up in the UK in spring 2020 to coordinate the mathematical sciences research community in supporting mathematical modelling of COVID-19. Each initiative had different primary aims and worked to maximise synergies between the various projects. We reflect on the lessons learnt, highlighting the key roles of pre-existing research collaborations and focal centres of coordination in contributing to the success of these initiatives. We conclude with recommendations about important ways in which the scientific research community could be better prepared for future pandemics. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics". [ABSTRACT FROM AUTHOR]

Immune checkpoint inhibitors (ICIs) introduced in recent years have revolutionized the treatment of many metastatic cancers. However, data suggest that treatment has benefits only in a limited percentage of patients, and that this is due to immune suppression of the tumor microenvironment (TME). Anti-tumor inflammatory macrophages (M1), which are attracted to the TME, are converted by tumor secreted cytokines, such as CSF-1, to pro-tumor anti-inflammatory macrophages (M2), or tumor associated macrophages (TAMs), which block the anti-tumor T cells. In the present paper we develop a mathematical model that represents the interactions among the immune cells and cancer in terms of differential equations. The model can be used to assess treatments of combination therapy of anti-PD-1 with anti-CSF-1. Examples are given in comparing the efficacy among different strategies for anti-CSF-1 dosing in a setup of clinical trials. • A model of M1 to M2 macrophages conversion by the cytokine CSF-1 is developed. • Treatment's efficacy & toxicity with combining anti-PD-1 and anti-CSF-1 is assessed. • The best strategy is to give anti-CSF-1 at larger amounts as early as possible. [ABSTRACT FROM AUTHOR]

The dynamics of swinging bells is a timely problem considered when the bell's supporting structures are designed or monitored. The geometry of a yoke and the magnitude of an excitation force are crucial parameters determining a yoke–bell–clapper system response for a given shape and size of the bell. This paper presents the novel yoke–bell–clapper system with variable geometry and adjustable excitation force. A mathematical model based on the existing prototype is introduced. The mathematical model is validated, and then the influence of the yoke geometry and excitation force on the system response is assessed. The simulations are done using a sample-based approach. The system that undergoes investigation is non-linear, piecewise, and discontinuous. The derived mathematical model can reliably predict the ringing scheme of a bell and associated reaction forces in the supports. • We propose a novel model of the yoke–bell–clapper system. • We validate the model based on the prototype rig. • We investigate forces transmitted to the structure by the yoke–bell–clapper system. • We use the sample-based method to perform the numerical calculation to show the system's response in a wide range of system's parameters. • We prove that the model is robust and allows us to predict the dynamics of the yoke–bell–clapper system. [ABSTRACT FROM AUTHOR]

The sucker rod string is eccentric due to the effect of wellbore bending. When the sucker rod string undergoes an eccentric motion within the wellbore containing viscoelastic fluid in the polymer flooding pumping wells, it is subjected to an alternating normally distributed load caused by viscoelastic fluid (NDLVF). In this paper, it is pointed out that the alternating NDLVF acting on the sucker rod string is the excitation of the transverse vibration of the sucker rod string. Moreover, the coupling relationship between the NDLVF and the transverse vibration displacement of the sucker rod string is considered. Based on the elastic vibration theory, the mechanical and mathematical model of the transverse vibration of a sucker rod string under the NDLVF in the curved wellbore is established. Then, the Runge-Kutta method is used to solve the simulation model, and parameter sensitivity analysis is carried out. The simulation results show that: (1) the NDLVF can significantly affect the transverse displacement of the sucker rod string and the rod-tubing contact force, which is an essential excitation for the transverse vibration of the sucker rod string in the polymer flooding pumping wells. (2) Due to the NDLVF presence, the contact collision between the rod string and tubing string occurs more frequently, and the rod-tubing contact force is increased. (3) The NDLVF effect on the transverse vibration of the sucker rod string is most noticeable near the neutral point of the sucker rod string. (4) With an increase in the polymer concentration, stroke length, and stroke frequency, the transverse vibration of the rod string becomes stronger. The transverse vibration simulation model of the sucker rod string under NDLVF in a curved wellbore plays a guiding role when analyzing rod-tubing eccentric wear and optimal allocation of a centralizer in the polymer flooding pumping wells. [ABSTRACT FROM AUTHOR]

Mode interaction in M/NEMS arouses many interests in enhancing functionality in recent years. In this paper, the dynamics of two mechanically coupled micro-resonators with frequency ratio approximately 1:3 for tuning driving strength is investigated experimentally and analytically. Mode interaction induced three stages of response, i.e., typical Duffing response, large half-flattened response and narrow full-flattened response, of the coupled resonators as driving strength increasing are observed. The amplitude relationship of two resonators for each stage is also obtained. The theoretical study based on the mathematical model successfully explains the previous observations. Almost 1-order enhancement of the amplitude stability in the response flattening range is observed finally, which makes the mechanical coupled micro-resonators brilliant candidate as an amplitude-sensing sensor. [ABSTRACT FROM AUTHOR]

• A novel DNA-structured model for cell-cycle analysis in cyclic hypoxia. • Cyclic hypoxia causes variation in the duration of the S phase. • Different mechanisms inhibit cell-cycle progression in chronic and cyclic hypoxia. • Cyclic hypoxia can result either in inhibition or slow down of the cell-cycle. New experimental data have shown how the periodic exposure of cells to low oxygen levels (i.e. , cyclic hypoxia) impacts their progress through the cell-cycle. Cyclic hypoxia has been detected in tumours and linked to poor prognosis and treatment failure. While fluctuating oxygen environments can be reproduced in vitro , the range of oxygen cycles that can be tested is limited. By contrast, mathematical models can be used to predict the response to a wide range of cyclic dynamics. Accordingly, in this paper we develop a mechanistic model of the cell-cycle that can be combined with in vitro experiments to better understand the link between cyclic hypoxia and cell-cycle dysregulation. A distinguishing feature of our model is the inclusion of impaired DNA synthesis and cell-cycle arrest due to periodic exposure to severely low oxygen levels. Our model decomposes the cell population into five compartments and a time-dependent delay accounts for the variability in the duration of the S phase which increases in severe hypoxia due to reduced rates of DNA synthesis. We calibrate our model against experimental data and show that it recapitulates the observed cell-cycle dynamics. We use the calibrated model to investigate the response of cells to oxygen cycles not yet tested experimentally. When the re-oxygenation phase is sufficiently long, our model predicts that cyclic hypoxia simply slows cell proliferation since cells spend more time in the S phase. On the contrary, cycles with short periods of re-oxygenation are predicted to lead to inhibition of proliferation, with cells arresting from the cell-cycle in the G2 phase. While model predictions on short time scales (about a day) are fairly accurate (i.e , confidence intervals are small), the predictions become more uncertain over longer periods. Hence, we use our model to inform experimental design that can lead to improved model parameter estimates and validate model predictions. [ABSTRACT FROM AUTHOR]

• An age-structured mathematical model on mumps outbreaks in Jiangsu, China is proposed and analyzed. • Three different stages of no vaccine, effectively controlled and resurgence stages are considered. • Patterns of mumps dynamics are simulated and compared based on data in Jiangsu from January 2005 to May 2019. • The time average basic reproduction number may be lower or over estimated the real one. • Changes in seasonal transmission patterns and demographic structures may be reasons of mumpsre-emerging. Measles, mumps and rubella (MMR) vaccine program was introduced in Jiangsu province of China in May 2008 and has been greatly contributed to decreasing of mumps cases. However, mumps has been resurging since May 2015. A number of studies have put forward that the resurgence of mumps is due to vaccine failure. In this paper, we investigated the other reasons for the resurging of mumps, such as the changes in seasonal transmission patterns and demographic structures, by using an age-structured mathematical model. We divided the history (January 2005 to May 2019) of mumps epidemics of Jiangsu province into three different stages: No vaccine stage (January 2005 to December 2008), effectively controlled stage (January 2009 to December 2014) and resurgence stage (January 2015 to May 2019). The features of mumps epidemics in three stages are compared under different demographic structures with same physical contact rate. The mumps transmission rate was increased in summer and dropped in November in stage III compared with that in stage I. The changes in demographic structures give a good explanation why the mumps outbreaked among children around 10 years old in stage I and around 5 years old in stage III. We have a conclusion that the vaccine failure, changes in seasonality and demographic structures were associated with the mumps outbreaks in recent years in Jiangsu province, China. We give the patterns of mumps dynamics considering age, vaccine, seasonality and demographic structures, which can help health program planners to implement more preventive interventions in mumps control during the period of higher risk of infection. [ABSTRACT FROM AUTHOR]

• The article is the first to describe a spatial mathematical model of myocardial infarction. • It is based on a network of complex interactions between inflammatory cells, cytokines and local cardiac myocytes. • The model predicts several useful new drug combinations. A heart attack, or acute myocardial infarction (MI) is caused by the acute occlusion of a coronary artery. MI is associated with 30% mortality; approximately half of the deaths occur prior to arrival at the hospital. Reperfusion therapy in the hospital is a medical treatment to restore blood flow through the blocked artery; treatment includes drugs and surgery. However, the damage to the heart muscles through the infarct area is permanent and there is additional damage around the infarct area due to inflammation or insufficient oxygen supply. Approximately half of the patients who survive MI are hospitalized again within one year after reperfusion treatment. In this paper we develop a mathematical model of MI and use it to assess the efficacy of drugs used, post reperfusion, to reduce the damage caused by inflammation in a region of the left ventricular wall surrounding the infarct area. The mathematical model, represented by a system of partial differential equations. The model variables include myocytes, endothelial cells, neutrophils, macrophages, fibroblasts and cytokines that play a role in the interactions among these cells. The drugs used to in the model include IL-1, TNF- α and TGF- β inhibitors, and the delivery of VEGF. The model is based on mice data. In particular, we find that immunomodulatory treatment with TNF- α and IL-1 inhibitors can significantly increase the low density of myocytes bordering the infarct area by 50–60% and decrease the abnormally high density of ECM in a region surrounding the infarct area. [ABSTRACT FROM AUTHOR]

• Presenting a new mathematical approach explaining the TFT threshold voltage shift. • Proposing a biologically plausible hybrid TFT-memristor neuromorphic synapse. • Improving the learning capabilities by proposing a triplet STDP learning synapse. New emerging nano-scale technologies like hydrogenated noncrystalline-silicon thin-film transistors (TFTs) and memristors, fabricated at low temperatures and over large areas, permit low-cost processing and 3D integration with CMOS cores. Here, we aim to propose a mathematical model which explains the memory-TFT threshold voltage shift due to the gate bias instability. Then, based on this mathematical approach, we propose a novel learning synapse composed of a voltage/flux driven memristor in parallel with a common-source memory-TFT with a memristive load. The proposed device realizes the triplet-based spike-timing-dependent plasticity rule (TSTDP) as a more realistic form of learning than the purely pair-based STDP (PSTDP). PSTDP is a synaptic learning rule which utilizes a constant-frequency pairing protocol to induce synaptic weight change and cannot explain the modification due to the frequency changes of spike pairs, and also the outcomes of triplet and quadruplet experiments. However, TSTDP improves the learning capabilities of the conventional PSTDP and reproduces the results of more electrophysiological experiments. In this paper, we apply various spike patterns like different-frequency and different-timing spike pairs, spike triplets, and quadruplets to the proposed device. Our simulations confirm a close match with the experimental data sets of real biological synapses. [ABSTRACT FROM AUTHOR]

• Rub-impact fault and model interval uncertainties are considered in a dual-rotor system using the non-probabilistic representations. • The nonlinear dynamical response with turning points, which is characterized as having multi-solution regions, is dealt with the polar angle interpolation method. • Performances of the polar angle interpolation method and the non-intrusive uncertainty analysis method are validated through deep comparisons. • Complicated uncertain behaviours are observed in the steady-state dynamical responses of the nonlinear system for various numerical cases under different conditions. This paper aims to study the nonlinear steady-state response of a dual-rotor system with rub-impact fault subject to unknown-but-bounded (UBB) uncertainties. Mathematical modelling of the non-linear dynamical system is carried out based on the Lagrangian formulation. The nonlinear dynamic response of the rubbing dual-rotor system without uncertainty is solved by using the multi-dimensional harmonic balance method coupled with the alternating frequency/time technique. The arc-length continuation is used to track the solution branches. To predict the response range subject to uncertainty, a non-intrusive surrogate model in conjunction with the polar angle interpolation (PAI) with efficiency enhancement is developed to track the propagations of parametric variabilities. The PAI is dedicated to dealing with collocations where the responses have multiple solutions. Effects of UBB variables in the physical model and fault-related parameters are investigated comprehensively. Different features of the variabilities in the steady-state responses are found under the typical uncertain degrees. The interval scanning method is used to validate the computation accuracy of the whole procedure. Moreover, the working mechanism of the PAI method is demonstrated via examples in detail. The results obtained in simulations can provide useful guidance for the nonlinear dynamic investigations and rub-impact fault diagnosis of dual-rotor systems under the UBB uncertainties. The proposed non-intrusive uncertainty quantification framework based on the PAI will also be beneficial to other nonlinear vibration problems where multiple solutions are involved. [ABSTRACT FROM AUTHOR]

• New analysis of the ligand-induced dimerisation process for VEGFR is presented. • A key idea in the mathematical model and analysis is kinetic binding cooperativity. • The nonlinear model is in contrast with the corresponding linear model for GPCRs. • Numerical and asymptotic analysis reveal insights into the underlying LID dynamics. • Our simulations show excellent fit to recent experimental data for VEGFR. The vascular endothelial growth factor (VEGF) receptor (VEGFR) system plays a role in cancer and many other diseases. It is widely accepted that VEGFR receptors dimerise in response to VEGF binding. However, analysis of these mechanisms and their implications for drug development still requires further exploration. In this paper, we present a mathematical model representing the binding of VEGF to VEGFR and the subsequent ligand-induced dimerisation. A key factor in this work is the qualitative and quantitative effect of binding cooperativity, which describes the effect that the binding of a ligand to a receptor has on the binding of that ligand to a second receptor, and the dimerisation of these receptors. We analyse the ordinary differential equation system at equilibrium, giving analytical solutions for the total amount of ligand bound. For time-course dynamics, we use numerical methods to explore possible behaviours under various parameter regimes, while perturbation analysis is used to understand the intricacies of these behaviours. Our simulation results show an excellent fit to experimental data, towards validating the model. [ABSTRACT FROM AUTHOR]