Explicit Mathematical Model Research Articles

Comparative analysis of dynamic changes in forest resources with RBF neural network and regression method

Forest resources are the most important natural resources; their dynamic changes (growth or decline) are affected by socio-economic factors, and to study their linkage is of great significance. However, the relationship between forest resources and social economic factors is normally a multivariate nonlinear relationship. There are difficulties in accurately analyzing it by using traditional multivariate-statistical methods. Also, its explicit mathematical model is inconvenient for intelligent management. In this paper, the radial basis function (RBF) neural network was introduced to study the relationship between the changes of forest resources and socio-economic factors and was evaluated by comparison with the traditional multiple-linear regression model. The results showed that the RBF neural network method can be applied in modeling the dynamic changes of forest resources and showed a higher prediction accuracy over the traditional statistical modeling approaches. At the same time, the RBF neural network can analyze and evaluate the importance of influencing factors simply and conveniently. The results provide a new way and show an application potential for the analysis and intelligent management in forest resources.

Measuring Splash Dispersal of a Major Wheat Pathogen in the Field

Capacity for dispersal is a fundamental fitness component of plant pathogens. Characterization of plant pathogen dispersal is important for understanding how pathogen populations change in time and space. We devised a systematic approach to measure and analyze rain splash-driven dispersal of plant pathogens in field conditions, using the major fungal wheat pathogen Zymoseptoria tritici as a case study. We inoculated field plots of wheat ( Triticum aestivum) with two distinct Z. tritici strains. Next, we measured disease intensity as counts of fruiting bodies (pycnidia) using automated image analysis. These measurements characterized primary disease gradients, which we used to estimate effective dispersal of the pathogen population. Genotyping of reisolated pathogen strains with strain-specific PCR confirmed the conclusions drawn from phenotypic data. Consistently with controlled environment studies, we found that the characteristic scale of dispersal is tens of centimeters. We analyzed the data using a spatially explicit mathematical model that incorporates the spatial extent of the source, rather than assuming a point source, which allows for a more accurate estimation of dispersal kernels. We employed bootstrapping methods for statistical testing and adopted a two-dimensional hypotheses test based on kernel density estimation, enabling more robust inference compared with standard methods. We report the first estimates of dispersal kernels of the pathogen in field conditions. However, repeating the experiment in other environments would lead to more robust conclusions. We put forward advanced methodology that paves the way for further measurements of plant pathogen dispersal in field conditions, which can inform spatially targeted plant disease management. [Formula: see text] Copyright © 2022 The Author(s). This is an open access article distributed under the CC BY 4.0 International license .

Atom transfer radical polymerization initiated by activator generated by electron transfer in emulsion media: a review of recent advances and challenges from an engineering perspective

Atom transfer radical polymerization (ATRP) is a powerful initiation technique that has been used successfully to create a variety of advanced materials. ATRP induced by a benign reducing agent (AGET ATRP) is gaining popularity in emulsion media. The use of emulsion AGET ATRP in a two-step experimental procedure opens up new possibilities for developing environmentally friendly, low-cost, and less toxic catalytic systems. However, no study has specifically addressed the difficulties associated with ligand solubility, ligand-surfactant compatibility, and stirring speed when emulsion AGET ATRP is performed. Furthermore, only a few experimental studies have looked for scaling-up emulsion AGET ATRP, and no explicit mathematical model for this particular system has been reported so far. In this review paper, we discuss the experimental work done so far for the emulsion AGET ATRP. In addition, we show the modern technologies that have been used to address the drawbacks of emulsion AGET ATRP. This review paper also discusses the fundamentals and recent advances in empirical and statistical models developed to better understand the complex mechanism of emulsion AGET ATRP.

Modelling the Darcy–Weisbach friction factor and the energy gradient of the lateral line*

AbstractThe objective was to adjust explicit mathematical models to determine the friction factor (f). Besides, an adaptation of the Blasius model is presented and an application of the Darcy–Weisbach equation to estimate the energy loss along the lateral line for four types of microsprinklers. f was determined by the model of Offor and Alabi and the model of Blasius for velocities between 0.5 to 3.0 m s−1 and internal pipe diameters of 0.0130, 0.0161, 0.0206, 0.0270, 0.0288, and 0.0368 m. The friction factor determined by Offor and Alabi was associated with the pipe diameters utilizing regression, and based on that an adaptation to the Blasius model was proposed. From the results of f, the energy and flow gradient along the lateral line for four NaanDanJain microsprinklers was simulated. The models of Offor and Alabi, Blasius, and Adapted Blasius showed excellent precision in determining f. The results of unit head loss, determined by the three mathematical models, showed dispersion close to zero among the pairs, showing a high correlation between the models (R2 = 0.99). The Blasius equation is the most suitable to be inserted into the Darcy–Weisbach model to determine the maximum length of the lateral line.

Genetic Algorithm and Deep Learning to Explore Parametric Trends in Nucleate Boiling Heat Transfer Data

Abstract Exploring parametric effects in pool boiling is challenging because the dependence of the resulting surface heat flux is often nonlinear, and the mechanisms can interact in complex ways. Historically, parametric effects in nucleate boiling processes have been deduced by fitting relations obtained from physical models to experimental data and from correlated trends in nondimensionalized data. Using such approaches, observed trends are often influenced by the framing of the analysis that results from the modeling or the collection of dimensionless variables used. Machine learning strategies can be attractive alternatives because they can be constructed either to minimize biases or to emphasize specific biases that reflect knowledge of the system physics. The investigation summarized here explores the use of machine learning methods as a tool for determining parametric trends in boiling heat transfer data and as a means for developing methods to predict boiling heat transfer. Results are presented that demonstrate how a genetic algorithm and deep learning can be used to extract heat flux dependencies of a binary mixture on wall superheat, gravity, Marangoni effects, and pressure. The results provide new insight into how gravity and Marangoni effects interact in boiling processes of this type. The results also demonstrate how machine learning tools can clarify how different mechanisms interact in the boiling process, as well as directly providing the ability to predict heat transfer performance for nucleate boiling. Each technique demonstrated clear advantages depending on whether speed, accuracy, or an explicit mathematical model was prioritized.

Coulombic effects on resolution of ion mobility spectrometry and its application in online qualitative analysis

Ion mobility spectrometry is an important gas analysis method used in the rapid detection field. However, due to a lacking of explicit mathematical model of ion peak, it is difficult to extract characteristic analyte peaks from a spectrum containing overlapping peaks to achieve online qualitative analysis. Here, we present an asymmetric peak model for processing ion mobility peaks. For the asymmetric peak model, the key is to accurately estimate the standard deviation of the peak model and the fitting function of the tailing edge. We focused on the Coulombic effects on resolution of ion mobility spectrometry based on a new hypothesis of ion cloud shape and derived a formula for calculating the standard deviation taking the initial pulse width, diffusion and Coulomb repulsion factors into account. The proposed asymmetric peak model combines the advantages of optimal physical and chemical interpretation and explicit mathematical meaning. A fast decomposition method based on the peak model was developed to decompose overlapping peaks. Two overlapping simulated data sets and one real data set (a mixture of acetone and methyl salicylate) were used to test the method. The results indicated that our proposed method successfully decomposed the overlapping spectrum into individual peaks and performed markedly better than other three available methods in terms of the execution time. The proposed method meets the requirements for online qualitative analysis.

Artificial intelligence and machine learning methods in predicting anti-cancer drug combination effects.

Drug combinations have exhibited promising therapeutic effects in treating cancer patients with less toxicity and adverse side effects. However, it is infeasible to experimentally screen the enormous search space of all possible drug combinations. Therefore, developing computational models to efficiently and accurately identify potential anti-cancer synergistic drug combinations has attracted a lot of attention from the scientific community. Hypothesis-driven explicit mathematical methods or network pharmacology models have been popular in the last decade and have been comprehensively reviewed in previous surveys. With the surge of artificial intelligence and greater availability of large-scale datasets, machine learning especially deep learning methods are gaining popularity in the field of computational models for anti-cancer drug synergy prediction. Machine learning-based methods can be derived without strong assumptions about underlying mechanisms and have achieved state-of-the-art prediction performances, promoting much greater growth of the field. Here, we present a structured overview of available large-scale databases and machine learning especially deep learning methods in computational predictive models for anti-cancer drug synergy prediction. We provide a unified framework for machine learning models and detail existing model architectures as well as their contributions and limitations, shedding light into the future design of computational models. Besides, unbiased experiments are conducted to provide in-depth comparisons between reviewed papers in terms of their prediction performance.

HCV Spread Kinetics Reveal Varying Contributions of Transmission Modes to Infection Dynamics.

The hepatitis C virus (HCV) is capable of spreading within a host by two different transmission modes: cell-free and cell-to-cell. However, the contribution of each of these transmission mechanisms to HCV spread is unknown. To dissect the contribution of these different transmission modes to HCV spread, we measured HCV lifecycle kinetics and used an in vitro spread assay to monitor HCV spread kinetics after a low multiplicity of infection in the absence and presence of a neutralizing antibody that blocks cell-free spread. By analyzing these data with a spatially explicit mathematical model that describes viral spread on a single-cell level, we quantified the contribution of cell-free, and cell-to-cell spread to the overall infection dynamics and show that both transmission modes act synergistically to enhance the spread of infection. Thus, the simultaneous occurrence of both transmission modes represents an advantage for HCV that may contribute to viral persistence. Notably, the relative contribution of each viral transmission mode appeared to vary dependent on different experimental conditions and suggests that viral spread is optimized according to the environment. Together, our analyses provide insight into the spread dynamics of HCV and reveal how different transmission modes impact each other.

Dynamic energy dispatch strategy for integrated energy system based on improved deep reinforcement learning

Dynamic energy dispatch is an integral part of the operation optimization of integrated energy systems (IESs). Most existing dynamic dispatch schemes depend heavily on explicit forecast or mathematical models of the future uncertainties. Due to the randomness of renewable energy generation and energy demands, these approaches are limited by the accuracy of forecasting or model. A novel model-free dynamic dispatch strategy for IES based on improved deep reinforcement learning (DRL) is proposed to solve the problem. The IES dynamic dispatch problem is formulated as a Markov decision process (MDP), in which the uncertainties of renewable generation, electric load and heat load are considered. For solving the MDP, an improved deep deterministic policy gradient (DDPG) algorithm using prioritized experience replay mechanism and L2 regularization is developed, so as to improve the policy quality and learning efficiency of the dispatch strategy. The proposed approach does not require any forecast information or distribution knowledge, and can adaptively respond to the stochastic fluctuations of the supply and demands. Simulation results show the proposed dispatch strategy has faster convergence and lower operating costs than original DDPG-based strategy. In addition, the advantages of the proposed approach in terms of cost-effectiveness and stochastic environmental adaptation are validated.

Non-simultaneous real-time hybrid simulation of a numerical and experimental mechanical system with moderate nonlinearities via iterative coupling based on Frequency Response Functions

The coupled simulation of numerical and real subsystems is sometimes called ‘hybrid substructuring’, ‘hardware in the loop (HIL)’, ‘cyberphysical simulation’, or ‘hybrid simulation’, and is an active field of research. In this publication, an iterative algorithm for a coupled simulation of a numerical subsystem and a real (experimental) one is presented. The term ‘iterative’ means that the subsystems are not computed or tested simultaneously but in loops one after the other. After each loop run, new control signals are computed so that the deviation of the coupling forces and displacements becomes smaller with each iteration. If the coupling quantities are equal, then the systems are coupled in a mechanical sense because of the cutting force principle. The proposed method works for quasi-static (slow speed) and dynamically reacting systems as well as for subsystems with moderate nonlinearities. The iterative character has several consequences: (1) No controllers are necessary. (2) The speed of the data exchange is not critical. (3) The method can only be applied to components whose properties do not change during the simulation (e.g. due to damage). Privacy between the two domains is guaranteed, as no explicit mathematical models in the sense of Finite Element (FE) structures or the like, but only frequency response functions, have to be exchanged. A possible application scenario could look as follows: An original equipment manufacturer (OEM) provides a web interface to a complex overall simulation model. A (geographically distant) supplier starts an iterative co-simulation with a somehow modified component (e.g. a bearing). Both sides can thus estimate the impact on the overall system. After explaining the theory, two examples are presented. The first concerns the coupled simulation of two pure numerical systems. In the second example, mixed numerical and experimental subsystems are coupled. Hence, a simple wheel suspension is considered, where the shock absorber is the real part on a test bench.

Prediction of seismic damage spectra using computational intelligence methods

Predicting seismic damage spectra, capturing both structural and earthquake features, is useful in performance-based seismic design and quantifying the potential seismic damage of structures. The objective of this paper is to accurately predict the seismic damage spectra using computational intelligence methods. For this purpose, an inelastic single-degree-of-freedom system subjected to a set of earthquake ground motion records is used to compute the (exact) spectral damage. The Park-Ang damage index is used to quantify the seismic damage. Both structural and earthquake features are involved in the prediction models where multi-gene genetic programming (MGGP) and artificial neural networks (ANNs) are applied. Common performance metrics were used to assess the models developed for seismic damage spectra, and indicated that their accuracy was higher than a corresponding model in the literature. Although the performance metrics revealed that the ANN model is more accurate than the MGGP model, the explicit MGGP-based mathematical model renders it more practical in quantifying the potential seismic damage of structures.

Natural strongholds for red squirrel conservation in Scotland

The Eurasian Red Squirrel (Sciurus vulgaris) is under threat from the invasive North American eastern Grey Squirrel (Sciurus carolinensis) with 80% of the remaining red squirrel populations in the British Isles found in Scotland. In this study we develop a spatially explicit mathematical model of the red and grey squirrel system and use it to assess the population viability of red squirrels across Scotland. In particular, we aim to identify existing forests – natural strongholds for red squirrels – that can successfully support red squirrels under UK Forestry Standard management and protect them from potential disease-mediated competition from grey squirrels. Our model results indicate that if current levels of grey squirrel control, which restrict or reduce the distribution of grey squirrels, are continued then there will be large expanses of forests in northern Scotland that support viable red squirrel populations. Model results that represent (hypothetical) scenarios where grey squirrel control no longer occurred indicated that grey squirrel range expansion and the process of red squirrel replacement would be slow. Model results for an assumed worst-case scenario where grey squirrels have expanded to all regions in Scotland identified forest regions – denoted natural strongholds – that could currently support red squirrels under UK Forestry Standard management practice. The results will be used to inform forest management policy and support a strategic review of red squirrel management by land management agencies and other stakeholders.

UAV attitude estimation based on MARG and optical flow sensors using gated recurrent unit

Three-dimensional attitude estimation for unmanned aerial vehicles is usually based on the combination of magnetometer, accelerometer, and gyroscope (MARG). But MARG sensor can be easily affected by various disturbances, for example, vibration, external magnetic interference, and gyro drift. Optical flow sensor has the ability to extract motion information from image sequence, and thus, it is potential to augment three-dimensional attitude estimation for unmanned aerial vehicles. But the major problem is that the optical flow can be caused by both translational and rotational movements, which are difficult to be distinguished from each other. To solve the above problems, this article uses a gated recurrent unit neural network to implement data fusion for MARG and optical flow sensors, so as to enhance the accuracy of three-dimensional attitude estimation for unmanned aerial vehicles. The proposed algorithm can effectively make use of the attitude information contained in the optical flow measurements and can also achieve multi-sensor fusion for attitude estimation without explicit mathematical model. Compared with the commonly used extended Kalman filter algorithm for attitude estimation, the proposed algorithm shows higher accuracy in the flight test of quad-rotor unmanned aerial vehicles.

Reproductive interference hampers species coexistence despite conspecific sperm precedence.

Negative interspecific mating interactions, known as reproductive interference, can hamper species coexistence in a local patch and promote niche partitioning or geographical segregation of closely related species. Conspecific sperm precedence (CSP), which occurs when females that have mated with both conspecific and heterospecific males preferentially use conspecific sperm for fertilization, might contribute to species coexistence by mitigating the costs of interspecific mating and hybridization. We discussed whether two species exhibiting CSP can coexist in a local environment in the presence of reproductive interference. First, using a behaviorally explicit mathematical model, we demonstrated that two species characterized by negative mating interactions are unlikely to coexist because the costs of reproductive interference, such as loss of mating opportunity with conspecific partners, are inevitably incurred when individuals of both species are present. Second, we experimentally examined differences in mating activity and preference in two Harmonia ladybird species known to exhibit CSP. These behavioral differences may lead to local extinction of H. yedoensis because of reproductive interference by H. axyridis. This prediction is consistent with field observations that H. axyridis uses various food sources and habitats whereas H. yedoensis is confined to a less preferred prey item and a pine tree habitat. Finally, by a comparative approach, we observed that niche partitioning or parapatric distribution, but not sympatric coexistence in the same habitat, is maintained between species with CSP belonging to a wide range of taxa, including vertebrates and invertebrates living in aquatic or terrestrial environments. Taken together, it is possible that reproductive interference may destabilize local coexistence even in closely related species that exhibit CSP.

Data Driven State Reconstruction of Dynamical System Based on Approximate Dynamic Programming and Reinforcement Learning

A data-driven approximation formulation for the state reconstruction problem of dynamical systems is presented in this paper. Without the assumption of an explicit mathematical model, the Hamilton–Jacobi–Bellman (HJB) based approach of a data-driven state reconstruction design method for monitoring and output-feedback control of dynamical systems is presented. The proposed state reconstruction design is based on a dynamic programming approach. To evaluate the proposed state reconstruction, computational experiments are conducted using only dynamical system model output data. The sensitivity of the algorithm parameters is also analyzed and discussed. The performance evaluation is analyzed in terms of the error metrics of the discrete linear quadratic regulator with output feedback under the value iteration algorithm through a reinforcement learning strategy.

CellBox: Interpretable Machine Learning for Perturbation Biology with Application to the Design of Cancer Combination Therapy.

Systematic perturbation of cells followed by comprehensive measurements of molecular and phenotypic responses provides informative data resources for constructing computational models of cell biology. Models that generalize well beyond training data can be used to identify combinatorial perturbations of potential therapeutic interest. Major challenges for machine learning on large biological datasets are to find global optima in a complex multidimensional space and mechanistically interpret the solutions. To address these challenges, we introduce a hybrid approach that combines explicit mathematical models of cell dynamics with a machine-learning framework, implemented in TensorFlow. We tested the modeling framework on a perturbation-response dataset of a melanoma cell line after drug treatments. The models can be efficiently trained to describe cellular behavior accurately. Even though completely data driven and independent of prior knowledge, the resulting de novo network models recapitulate some known interactions. The approach is readily applicable to various kinetic models of cell biology. A record of this paper's Transparent Peer Review process is included in the Supplemental Information.

STABILITY ANALYSIS OF THIN BAR SUBJECTED TO A LOADING SYSTEM WITHIN COMPLEX BOUNDARY CONDITIONS

The research on determination of the statical and lateral stability region of thin bar subjected to a loading system within the complex boundary conditions has been studied in this paper. The loading system includes axial force, uniformly distributed loads and bending moment at both ends of the bar. Both ends of the bar are embeded steadily, while in the literature elsewhere they are simply pin supports. Energetic and analytical methods were used to solve the proposed problem. Having said that, the authors have developed an explicit mathematical model that allows calculating and analysing the critical state of thin bar under the abovementioned complex loading system. Besides, the numerical calculation to verify the reliability of the obtained model was also carried out and it turned out the relatively insignificant error. The outcomes of this paper could be used broadly for mechanical and civil engineering, as well as many others in the engineering area.

Prediction Mathematic Model and Influencing Factors of Contact Stress of Cylindrical Gear with Arc Tooth

Given the absence of a theoretical formula to analyze the influence of parameters on the contact stress of cylindrical gear with arc tooth, an explicit mathematical model of cylindrical gear with arc tooth between the design parameters and the contact stress is established based on Kriging surrogate model. The parameters of the variation function of Kriging model are optimized by using the whale optimization algorithm (WOA), and the explicit mathematical model accuracy between the design parameters and the contact stress of the gear is in turn optimized by the improved Kriging surrogate model. The influence of design parameters on the contact stress of cylindrical gear with arc tooth is analyzed based on the established mathematical model. The proposed algorithm was realized via the programming platform MATLAB; the simulation results indicate that the precision evaluation indexes (the correlation coefficient (R2), root mean square error (RMSE), and the relative maximum absolute error (RMAE)) of the proposed Kriging model are improved, in addition to the error range which is narrowed from (−2, 4) to (0, 3). As the tooth width, modulus, pressure angle, and tooth line radius increased, the contact stress of the cylindrical gear with arc tooth gear declined, which was negatively correlated with the design parameter. The amplitude of contact stress of the cylindrical gear with arc tooth was the largest due to the change of tooth radius, followed by the change of modulus, while the influence of tooth width was less. Finally, the influence of modulus-tooth line radius interaction and pressure angle-tooth line radius interaction on contact stress of cylindrical gear with arc tooth was significant.

Estimating the COVID-19 Death Toll by Considering the Time-Dependent Effects of Various Pandemic Restrictions

COVID-19, known as Coronavirus disease 2019, is caused by a coronavirus called SARS-CoV-2. As coronavirus restrictions ease and cause changes to social and business activities around the world, and in the United States in particular, including social distancing, reopening states, reopening schools, and the face mask mandates, COVID-19 outbreaks are on the rise in many states across the United States and several other countries around the world. The United States recorded more than 1.9 million new infections in July, which is nearly 36 percent of the more than 5.4 million cases reported nationwide since the pandemic began, including more than 170,000 deaths from the disease, according to data from Johns Hopkins University as of 16 August 2020. In April 2020, the author of this paper presented a model to estimate the number of deaths related to COVID-19, which assumed that there would be no significant change in the COVID-19 restrictions and guidelines in the coming days. This paper, which presents the evolved version of the previous model published in April, discusses a new explicit mathematical model that considers the time-dependent effects of various pandemic restrictions and changes related to COVID-19, such as reopening states, social distancing, reopening schools, and face mask mandates in communities, along with a set of selected indicators, including the COVID-19 recovered cases and daily new cases. We analyzed and compared the modeling results to two recent models based on several model selection criteria. The model could predict the death toll related to the COVID-19 virus in the United States and worldwide based on the data available from Worldometer. The results show the proposed model fit the data significantly better for the United States and worldwide COVID-19 data that were available on 16 August 2020. The results show very encouraging predictability that reflected the time-dependent effects of various pandemic restrictions for the proposed model. The proposed model predicted that the total number of U.S. deaths could reach 208,375 by 1 October 2020, with a possible range of approximately 199,265 to 217,480 deaths based on data available on 16 August 2020. The model also projected that the death toll could reach 233,840 by 1 November 2020, with a possible range of 220,170 to 247,500 American deaths. The modeling result could serve as a baseline to help decision-makers to create a scientific framework to quantify their guidelines related to COVID-19 affairs. The model predicted that the death toll worldwide related to COVID-19 virus could reach 977,625 by 1 October 2020, with a possible range of approximately 910,820 to 1,044,430 deaths worldwide based on data available on 16 August 2020. It also predicted that the global death toll would reach nearly 1,131,000 by 1 November 2020, with a possible range of 1,030,765 to 1,231,175 deaths. The proposed model also predicted that the global death toll could reach 1.47 million deaths worldwide as a result of the SARS CoV-2 coronavirus that causes COVID-19. We plan to apply or refine the proposed model in the near future to further study the COVID-19 death tolls for India and Brazil, where the two countries currently have the second and third highest total COVID-19 cases after the United States.

Abstract 2102: Interpretable machine learning for perturbation biology

Abstract Systematic perturbation of cells followed by comprehensive measurements of molecular and phenotypic responses provides an informative data resource for constructing computational models of cell biology. Models that generalize well beyond training data can be used to identify combinatorial perturbations of potential therapeutic interest. Major challenges for machine learning on large biological datasets are to find global optima in an enormously complex multi-dimensional solution space and to mechanistically interpret the solutions. To address these challenges, we introduce a hybrid approach that combines explicit mathematical models of dynamic cell biological processes with a machine learning framework, implemented in Tensorflow. We tested the modeling framework on a perturbation-response dataset for a melanoma cell line after drug treatments. The models can be efficiently trained to accurately describe cellular behavior, as tested by cross-validation. Even though completely data-driven and independent of prior knowledge, the resulting de novo network models recapitulate known interactions. The main predictive application of our work is the identification of combinatorial candidates for cancer therapy. This approach is readily applicable to a wide range of kinetic models of cell biology. Citation Format: Judy Shen, Bo Yuan, Augustin Luna, Anil Korkut, Debora Marks, John Ingraham, Chris Sander. Interpretable machine learning for perturbation biology [abstract]. In: Proceedings of the Annual Meeting of the American Association for Cancer Research 2020; 2020 Apr 27-28 and Jun 22-24. Philadelphia (PA): AACR; Cancer Res 2020;80(16 Suppl):Abstract nr 2102.