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Pulp-and-paper mills produce various types of contaminants and a significant amount of wastewater depending on the type of processes used in the plant. Since the generated wastewaters can be potentially polluting and very dangerous, they should be treated in wastewater treatment plants before being released to the environment. This paper reviews different wastewater treatment processes used in the pulp-and-paper industry and compares them with respect to their contaminant removal efficiencies and the extent of greenhouse gas (GHG) emission. It also evaluates the impact of operating parameters on the performance of different treatment processes. Two mathematical models were used to estimate GHG emission in common biological treatment processes used in the pulp-and-paper industry. Nutrient removal processes and sludge treatment are discussed and their associated GHG emissions are calculated. Although both aerobic and anaerobic biological processes are appropriate for wastewater treatment, their combination known as hybrid processes showed a better contaminant removal capacity at higher efficiencies under optimized operating conditions with reduced GHG emission and energy costs. [ABSTRACT FROM AUTHOR]

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]

Abstract: We developed a new meat product referred to as meat paper, which is edible paper made from beef, and the purpose of this study was to establish optimal conditions for making meat paper. Response surface methodology was used to model and optimize responses (folding test, springiness and cohesiveness). Dehydration conditions, such as drying temperature (46.6–63.4 °C) and drying time (78.0–138.0 min), and sample cutting time (13.2–46.8 s) were selected as the main processing conditions in the making of meat paper. Optimal conditions for the minimum folding test (cm), maximum springiness (%) and cohesiveness (%) of the meat paper were established. We found four solutions with the following conditions: 17.2–19.2 s of sample cutting time, 52.6 °C of drying temperature and 123.0–125.0 min of drying time. We then successfully made meat paper under these conditions and confirmed various desirable properties of this product. [Copyright &y& Elsevier]

Abstract: This study describes the validation of a new electronic appetite rating system, and a statistical variance model for visual analogue scale (VAS) research. Thirty volunteers rated hunger, fullness, desire to eat, prospective intake, thirst and liking on 100mm paper VAS and on 70mm electronic VAS presented on a Dell™ Pocket PC, after consuming breakfast, in a repeated trial. The electronic method was comparable in relative accuracy and reproducibility to the paper method, with weak differences between tests (within-subject SD≤14mm). The data obtained were used to generate a model for VAS data variability. [Copyright &y& Elsevier]

In 2008, the National Institutes of Health's (NIH) Undiagnosed Disease Program (UDP) was initiated to provide diagnoses for individuals who had long sought one without success. As a result of two international conferences (Rome 2014 and Budapest 2015), the Undiagnosed Diseases Network International (UDNI) was established, modeled in part after the NIH UDP. Undiagnosed diseases are a global health issue, calling for an international scientific and healthcare effort. To meet this demand, the UDNI has built a consensus framework of principles, best practices and governance; the Board of Directors reflects its international character, as it includes experts from Australia, Canada, Hungary, Italy, Japan and the USA. The UDNI involves centers with internationally recognized expertise, and its scientific resources and know-how aim to fill the knowledge gaps that impede diagnosis. Consequently, the UDNI fosters the translation of research into medical practice. Active patient involvement is critical; the Patient Advisory Group is expected to play an increasing role in UDNI activities. All information for physicians and patients will be available at the UDNI website. [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]

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 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 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]

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]

• 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]

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]

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]

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]

• 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]

• 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]

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]

A subsoiler is an important implement in no-tillage agriculture that can keep the soil in a good condition and increase crop yields. The prediction and reduction of the draught force of subsoilers are vital for improving the efficiency of subsoilers and saving energy. In this paper, a mathematical-analytical model considering the subsoiler geometry, soil properties and working conditions was developed for predicting the draught force of a curved subsoiler. In addition, three curved subsoilers that were adapted for three different working depths were designed according to the model to reduce the draught force and energy consumption. Field experiments were conducted to validate the model and compare the draught force, soil disturbance area and specific resistance of the designed subsoilers with conventional ones. The results showed that the correlations between the measured and predicted draught force, soil disturbance area and specific resistance were significant, which meant that the model could be used to predict the performance of a curved subsoiler. The three designed subsoilers had smaller draught forces and specific resistances than those of conventional subsoilers at their designed working depths, so the designed subsoilers exhibited better performance at their designed working depths than conventional subsoilers. Therefore, the model developed in this paper was useful for predicting the draught force of curved subsoilers and designing a subsoiler with low specific resistance. • It is efficient to design subsoilers according to required tillage depths. • A model can be used to design curved subsoilers with low specific resistance. • Subsoilers exhibit better performance at their designed working depths. [ABSTRACT FROM AUTHOR]

• Philip Maini has made multiple significant contributions to the field of Mathematical Enzyme Kinetics. • Philip Maini has also contributed to the field by mentoring young researchers. • The Quasi-Steady State Assumption has now been expanded to include just about every possible initial condition. Modelling enzyme kinetics has a long history, as one of the earliest areas where mathematics was utilized to understand biological (in this case, biochemical) phenomena. By using differential equations and the law of mass action, many researchers have discovered information about the mechanisms of enzyme workings in the more than 100 years since Leonor Michaelis and Maud Menten published their classic paper in 1913. This work uses he laws obeyed by molecules during a reaction, translates them into mathematical equations, and then compares the results predicted by the equations to data obtained in laboratory conditions. This can inform whether the mechanism used to create the mathematical model is consistent with experimental results. Philip K. Maini has contributed to several significant results in the field of mathematical modelling in enzyme kinetics. Along with his collaborators, he has published results analyzing and extending the Quasi-Steady State Assumption, applying it to special enzyme reactions, and considering special conditions. This review paper will provide an overview of the contributions made by PK Maini to the field of modelling enzyme kinetics, summarize the main results and discuss their significance. [ABSTRACT FROM AUTHOR]

Abstract The present comment concerns some doubtful results included in the above paper. [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]

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]

While facultative sex is common in sexually reproducing species, for reasons of tractability most mathematical models assume that such sex is asynchronous in the population. In this paper, we develop a model of switching environments to instead capture the effect of an entire population transitioning synchronously between sexual and asexual modes of reproduction. We use this model to investigate the evolution of the number of self-incompatible mating types in finite populations, which empirically can range from two to thousands. When environmental switching is fast, we recover the results of earlier studies that implicitly assumed populations were engaged in asynchronous sexual reproduction. However when the environment switches slowly, we see deviations from previous asynchronous theory, including a lower number of mating types at equilibrium and bimodality in the stationary distribution of mating types. We provide analytic approximations for both the fast and slow switching regimes, as well as a numerical scheme based on the Kolmogorov equations for the system to quickly evaluate the model dynamics at intermediate parameters. Our approach exploits properties of integer partitions in number theory. We also demonstrate how additional biological processes such as selective sweeps can be accounted for in this switching environment framework, showing that beneficial mutations can further erode mating type diversity in synchronous facultatively sexual populations. [ABSTRACT FROM AUTHOR]

Highlights • This paper focuses on the implementation of motion control for active suspension systems using a novel scheme of model-free finite-time tracking control method. • The proposed strategy facilitates the realization since the system plant modeling is not needed. • Unlike the existing control methods, the proposed disturbance compensator is continuous and finite-time convergent, which shows a great potential in application to practical suspension systems. • The advantage of the presented control algorithm is verified via comparative investigation, especially the comparison of the existing extended state observer-based feedback control scheme. • Comparative experimental studies are presented to confirm the effectiveness and superiority of the proposed control strategy over the traditional methods. Abstract This paper focuses on the implementation of motion control for active suspension systems using a novel scheme of model-free finite-time tracking control method. The proposed strategy facilitates the realization since the system plant modeling is not needed. Correspondingly, the suspension vertical dynamics including external disturbances are estimated by the time-delay estimation, and its estimated error is compensated by the integral sliding mode control scheme. Theoretical analysis proves that the sliding mode and desired system dynamics can achieve a finite time convergence performance with continuous control law. In active suspension control, the continuous control law contributes to preventing the unexpected chattering in practical implementation. The advantage of the presented control algorithm is verified via comparative investigation, especially the comparison of the existing extended state observer-based feedback control scheme, which requires a high-gain observer to realize the desired dynamics. Comparative experimental studies are presented to confirm the effectiveness and superiority of the proposed control strategy over the traditional methods. [ABSTRACT FROM AUTHOR]

Abstract In this paper, motivated by diffraction of traveling light waves, a simple mathematical model is proposed, both for the multivariate super-resolution problem and the problem of blind-source separation of real-valued exponential sums. This model facilitates the development of a unified theory and a unified solution of both problems in this paper. Our consideration of the super-resolution problem is aimed at applications to fluorescence microscopy and observational astronomy, and the motivation for our consideration of the second problem is the current need of extracting multivariate exponential features in magnetic resonance spectroscopy (MRS) for the neurologist and radiologist as well as for providing a mathematical tool for isotope separation in Nuclear Chemistry. The unified method introduced in this paper can be easily realized by processing only finitely many data, sampled at locations that are not necessarily prescribed in advance, with computational scheme consisting only of matrix-vector multiplication, peak finding, and clustering. [ABSTRACT FROM AUTHOR]

Abstract Let M be a 3-connected binary matroid; M is internally 4-connected if one side of every 3-separation is a triangle or a triad, and M is (4 , 4 , S) -connected if one side of every 3-separation is a triangle, a triad, or a 4-element fan. Assume M is internally 4-connected and that neither M nor its dual is a cubic Möbius or planar ladder or a certain coextension thereof. Let N be an internally 4-connected proper minor of M. Our aim is to show that M has a proper internally 4-connected minor with an N -minor that can be obtained from M either by removing at most four elements, or by removing elements in an easily described way from a special substructure of M. When this aim cannot be met, the earlier papers in this series showed that, up to duality, M has a good bowtie, that is, a pair, { x 1 , x 2 , x 3 } and { x 4 , x 5 , x 6 } , of disjoint triangles and a cocircuit, { x 2 , x 3 , x 4 , x 5 } , where M \ x 3 has an N -minor and is (4 , 4 , S) -connected. We also showed that, when M has a good bowtie, either M \ x 3 , x 6 has an N -minor and M \ x 6 is (4 , 4 , S) -connected; or M \ x 3 / x 2 has an N -minor and is (4 , 4 , S) -connected. In this paper, we show that, when M \ x 3 , x 6 has no N -minor, M has an internally 4-connected proper minor with an N -minor that can be obtained from M by removing at most three elements, or by removing elements in a well-described way from a special substructure of M. This is a final step towards obtaining a splitter theorem for the class of internally 4-connected binary matroids. [ABSTRACT FROM AUTHOR]

Fractional derivative is increasingly being deployed to improve existing mathematical models due to its unique capability in describing anomalous behavior and memory effects which are common characteristics of natural phenomena. Improved vibration analysis has been accomplished by introducing fractional derivatives to model viscoelastic damping and vibration propagation through complex media and much research has been carried out to date. However, much of these existing research efforts have been sporadic to the best and there remains a pressing need to develop a consistent and systematic theoretical framework for vibration analysis of fractional systems to synergize for more productive and coordinated efforts in the area. This paper seeks to address some fundamental issues to facilitate further development such as the definition of general form of a fractional vibration system, its eigenvalue problem and methods of solution, definition of frequency response functions and applicability of conventional modal analysis, equivalent eigensystem and its more efficient eigensolution. With these important issues being resolved to clear the myth, vibration studies of fractional systems can be encouraged and expected to grow in a more fruitful direction. New methods developed and concepts discussed in the paper have all been validated through realistic numerical case studies based on a practical GARTEUR structure with viscoelastic supports modeled using fractional derivatives. [ABSTRACT FROM AUTHOR]

Abstract Let k ˜ be a cubic extension of Q. For quadratic fields F , let L = F ⋅ k ˜. In this paper and its companion paper, we prove that with a certain cohomological invariant i (F) , lim X → ∞ ⁡ X − 2 ∑ 0 < ± Δ F < X h L R L (h F R F) − 1 (1 + i (F) − 1) converges to a positive constant which is given by an Euler product. [ABSTRACT FROM AUTHOR]

Abstract We derive new bounds for moments of the error in the Sato–Tate law over families of elliptic curves. Our estimates are stronger than those obtained in [4] and [5] for the first and second moment, but this comes at the cost of larger ranges of averaging. As applications, we deduce new almost-all results for the said errors and a conditional Central Limit Theorem on the distribution of these errors. Our method is different from those used in the above-mentioned papers and builds on recent work by the second-named author and K. Sinha [21] who derived a Central Limit Theorem on the distribution of the errors in the Sato–Tate law for families of cusp forms for the full modular group. In addition, identities by Birch and Melzak play a crucial rule in this paper. Birch's identities connect moments of coefficients of Hasse–Weil L -functions for elliptic curves with the Kronecker class number and further with traces of Hecke operators. Melzak's identity is combinatorial in nature. [ABSTRACT FROM AUTHOR]

Highlights • The existent models of wound healing angiogenesis do not fully described the process. • Several advantages and disadvantages of current angiogenesis models are reviewed. • Computational models may reduce the use of expensive and time-consuming methodologies. • Upcoming models should include vascular network remodelling and ECM components. Abstract The occurrence of wounds is a main health concern in Western society due to their high frequency and treatment cost. During wound healing, the formation of a functional blood vessel network through angiogenesis is an essential process. Angiogenesis allows the reestablishment of the normal blood flow, the sufficient exchange of oxygen and nutrients and the removal of metabolic waste, necessary for cell proliferation and viability. Mathematical and computational models provide new tools to improve the healing process. In fact, over the last thirty years, in silico models have been continuously formulated to describe the effect of several biological and mechanical factors in angiogenesis during wound healing. Additionally, with different levels of complexity, these models allow coupling the human skin structure, to distinct cell types and growth factors, to study extracellular matrix composition and to understand its deformation. This paper discusses how in silico models, which are more economical and less time-consuming comparatively to laboratory methodologies, can help test new strategies to promote/optimize angiogenesis. The continuum, cell-based and hybrid mathematical models of wound healing angiogenesis are reviewed in the present paper, in order to identify possible improvements. Accordingly, the development of higher dimension models incorporating multiscale analysis at molecular, cellular and tissue level remains a challenge that future models should consider. [ABSTRACT FROM AUTHOR]

Abstract An effective and efficient stewardship of natural resources requires consistency across all decision-informing approaches and components involved, i.e., managerial, governmental, political, and legal. To achieve this consistency, these elements must be aligned under an overarching management goal that is consistent with current and well-accepted knowledge. In this article, we investigate the adoption by the US Bureau of Ocean Energy Management of an environmental resilience-centered system that manages for resilience of marine ecological resources and its associated social elements. Although the framework is generally tailored for this Bureau, it could also be adapted to other federal or non-federal organizations. This paper presents a dynamic framework that regards change as an inherent element of the socio-ecological system in which management structures, e.g., federal agencies, are embedded. The overall functioning of the management framework being considered seeks to mimic and anticipate environmental change in line with well-accepted elements of resilience-thinking. We also investigate the goal of using management for resilience as a platform to enhance socio-ecological sustainability by setting specific performance metrics embedded in pre-defined and desired social and/or ecological scenarios. Dynamic management frameworks that couple social and ecological systems as described in this paper can facilitate the efficient and effective utilization of resources, reduce uncertainty for decision and policy makers, and lead to more defensible decisions on resources. Highlights • A resilience-based framework is studied for efficient natural resource management. • The management framework is expanded and adapted to a specific organization. • Nested panarchies are used to couple social and ecological sub-systems. • The environmental management framework is used to analyze two practical examples. • The management framework could be adapted to other organizations or groups of them. [ABSTRACT FROM AUTHOR]

Abstract There is the paper by H. Tietze published in 1905 on differential transcendence of solutions of difference Riccati equations. In this paper, we clarify the essence of Tietze's treatment and make it purely algebraic. As an application, the q -Airy equation is studied. [ABSTRACT FROM AUTHOR]

This paper presents a new method to diagnose half broken rotor bar (BRB) fault in induction motor drive, running under various load conditions using a variable frequency drive (VFD). VFDs are commonly used in industries to improve motor’s efficiency, but at the same time it generates noise and this noise modulates with the line current. Noise leads to poor signal to noise ratio (SNR) as a result motor’s fault diagnosis using current monitoring becomes a challenging task, especially when the fault is at incipient stage. One such case of half broken rotor bar (BRB), has been discussed in this paper. Conventional techniques like motor current signature analysis (MCSA) is found to be ineffective in detecting half BRB fault at normal load condition. In this paper authors have developed an algorithm that generates a pseudo-spectrum of square of the current signal, using multiple signal classification (MUSIC) techniques. The square of current signal generates more BRB fault frequency components and helps in easily diagnosing the fault. These fault frequency components are detected using the proposed algorithm. The work has been experimentally validated at various load conditions. [ABSTRACT FROM AUTHOR]

An important point in looking for period solutions of the Camassa–Holm equation is to understand the associated spectral problem y ″ = 1 4 y + λ m ( t ) y . The first aim of this paper is to study the dependence of eigenvalues for the periodic Camassa–Holm Equation on potentials as an infinitely dimensional parameter. To be precise, we prove that as nonlinear functionals of potentials, eigenvalues for the periodic Camassa–Holm Equation are continuous in potentials with respect to the weak topologies in the L p Lebesgue spaces. The second aim of this paper is to find the optimal lower bound of the lowest eigenvalue for the periodic Camassa–Holm Equation when the L 1 norm of potentials are given. In order to make our results more applicable, we will find the optimal lower bound for the lowest eigenvalue in the more general setting of measure differential equations. [ABSTRACT FROM AUTHOR]

In this paper equilibrium measures in the presence of external fields created by fixed charges are analyzed. These external fields are a particular case of the so-called rational external fields (in the sense that their derivatives are rational functions). Along with some general results, a thorough analysis of the particular case of two fixed negative charges (“attractors”) is presented; indeed, the main result of the paper deals with this particular case. As for the main tools used, this paper is a natural continuation of [31] , where polynomial external fields were thoroughly studied, and [37] , where rational external fields with a polynomial part were considered. However, the absence of the polynomial part in the external fields analyzed in the current paper adds a considerable difficulty to solve the problem and justifies its separated treatment; moreover, it is noteworthy to point out the simplicity and beauty of the results obtained. [ABSTRACT FROM AUTHOR]

The Finite Volume method with Exact two-material Riemann Problems (FIVER) is both a computational framework for multi-material flows characterized by large density jumps, and an Embedded Boundary Method (EBM) for computational fluid dynamics and highly nonlinear Fluid–Structure Interaction (FSI) problems. This paper deals with the EBM aspect of FIVER. For FSI problems, this EBM has already demonstrated the ability to address viscous effects along wall boundaries, and large deformations and topological changes of such boundaries. However, like for most EBMs – also known as immersed boundary methods – the performance of FIVER in the vicinity of a wall boundary can be sensitive with respect to the position and orientation of this boundary relative to the embedding mesh. This is mainly due to ill-conditioning issues that arise when an embedded interface becomes too close to a node of the embedding mesh, which may lead to spurious oscillations in the computed solution gradients at the wall boundary. This paper resolves these issues by introducing an alternative definition of the active/inactive status of a mesh node that leads to the removal of all sources of potential ill-conditioning from all spatial approximations performed by FIVER in the vicinity of a fluid–structure interface. It also makes two additional contributions. The first one is a new procedure for constructing the fluid–structure half Riemann problem underlying the semi-discretization by FIVER of the convective fluxes. This procedure eliminates one extrapolation from the conventional treatment of the wall boundary conditions and replaces it by an interpolation, which improves robustness. The second contribution is a post-processing algorithm for computing quantities of interest at the wall that achieves smoothness in the computed solution and its gradients. Lessons learned from these enhancements and contributions that are triggered by the new definition of the status of a mesh node are then generalized and exploited to eliminate from the original version of the FIVER method its sensitivities with respect to both of the position and orientation of the wall boundary relative to the embedding mesh, while maintaining the original definition of the status of a mesh node. This leads to a family of second-generation FIVER methods whose performance is illustrated in this paper for several flow and FSI problems. These include a challenging flow problem over a bird wing characterized by a feather-induced surface roughness, and a complex flexible flapping wing problem for which experimental data is available. [ABSTRACT FROM AUTHOR]

This paper investigates the application of Hierarchical Bayesian model updating for uncertainty quantification and response prediction of civil structures. In this updating framework, structural parameters of an initial finite element (FE) model (e.g., stiffness or mass) are calibrated by minimizing error functions between the identified modal parameters and the corresponding parameters of the model. These error functions are assumed to have Gaussian probability distributions with unknown parameters to be determined. The estimated parameters of error functions represent the uncertainty of the calibrated model in predicting building’s response (modal parameters here). The focus of this paper is to answer whether the quantified model uncertainties using dynamic measurement at building’s reference/calibration state can be used to improve the model prediction accuracies at a different structural state, e.g., damaged structure. Also, the effects of prediction error bias on the uncertainty of the predicted values is studied. The test structure considered here is a ten-story concrete building located in Utica, NY. The modal parameters of the building at its reference state are identified from ambient vibration data and used to calibrate parameters of the initial FE model as well as the error functions. Before demolishing the building, six of its exterior walls were removed and ambient vibration measurements were also collected from the structure after the wall removal. These data are not used to calibrate the model; they are only used to assess the predicted results. The model updating framework proposed in this paper is applied to estimate the modal parameters of the building at its reference state as well as two damaged states: moderate damage (removal of four walls) and severe damage (removal of six walls). Good agreement is observed between the model-predicted modal parameters and those identified from vibration tests. Moreover, it is shown that including prediction error bias in the updating process instead of commonly-used zero-mean error function can significantly reduce the prediction uncertainties. [ABSTRACT FROM AUTHOR]

In this paper, the dynamic effect of the viscoelastic behavior of PE100 material, on the transient flow in a relatively long pipe, has been studied. At first, to study the transient flow in pipes with fluid structure interaction (FSI), two mathematical models, i.e., fully coupled four equation model and simplified two equation model, have been developed. The method of characteristics has been used to solve the model. Then, we have demonstrated that the viscoelastic behavior of PE100 plays a primordial role in the damping of the water hammer phenomenon. It has a dynamic effect to cause the decrease of pressure wave velocity with increase of pressure along the wave front. At the end of the paper, It has been shown that the coupled model with FSI does not introduce many changes from the simplified viscoelastic model. [ABSTRACT FROM AUTHOR]

The German mathematician Olaus Henrici, 1 who was born in Denmark in 1840, studied engineering and mathematics in Germany before making his career in London. Initially, and for only a short time, he worked in an engineering business. He subsequently took on academic positions, first at University College London and then, from 1884, at the newly formed Central Institution (later Central Technical College) where he established a Laboratory of Mechanics. While at University College he became an active promoter of pure geometry and a producer of models of surfaces. In this paper I explore the geometrical side of Henrici's work, setting it into the context of his career and arguing that his interdisciplinary background was a key factor in his success as a creator of models. [ABSTRACT FROM AUTHOR]

• A review on solving nonlinear hyperbolic systems of PDEs containing Dirac δ measures. • A review on α -product applications to some nonlinear models arising in mathematical physics. • Under certain conditions, δ waves in the Klein-Gordon equation behave like classical solitons in the sine-Gordon equation. The present paper studies the interaction of Dirac δ -waves in models ruled by the nonlinear Klein-Gordon equation u t t − c 2 u x x = ϕ (u) , where c > 0 is a real number and ϕ is an entire function taking real values on the real axis. Such study is made using a product of distributions that both extends the meaning of ϕ (u) for certain distributions u and allows the definition of a solution concept consistent with the classical solution concept. From such study, it emerges that in several nonlinear Klein-Gordon equations Dirac δ -waves behave like classical solitons in the sine-Gordon equation. As particular cases, this work examines the phi-four equation and the sine-Gordon equation. [ABSTRACT FROM AUTHOR]

Network-on-chip (NoC) is an integral part of many-core microprocessors. Performance analysis of network-on-chip directly affects the performance of the microprocessor. In this paper we propose a mathematical model to represent packet flow in an NoC as an open feed-forward queuing network. We study the performance of NoC by varying different parameters that includes packet injection rate, packet size, buffer size and number of virtual channels. We also discuss how different flow control algorithms, injection processes, traffic patterns can be incorporated in our model. Apart from the speedup achieved by our model, we also demonstrate that our model can be used to explore various configurations of NoC with minimal error. • We model Network-on-Chip as an open feed-forward queuing network. • We analysed and evaluated NoC under several configurations containing different traffic patterns, injection process and routing algorithms. • Analytical results were validated against simulation results from Booksim simulator. • We showed that numerical computation using analytical model has a speedup of 20 compared to simulations. [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]

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]

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]