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• Three driver mutations in the genome of lung stem cells are required in the development of lung cancer. • There is a gender difference in the development of lung cancer. • Increased carcinogens control efforts in early life will be needed to further slow lung cancer risk. In this paper, we propose a stochastic multistage model that incorporates clonal expansion of premalignant cells and mutational events. Using the age-specific lung cancer as the test system, the proposed model is used to fit the incidence data in the Surveillance, Epidemiology, and End Results (SEER) registry. We first use the model with different numbers of mutations to fit the data of all lung cancer patients. Our results demonstrate that, although from two to six driver mutations in the genome of lung stem cells are reasonable for normal lung stem cells to become a malignant cell, three driver mutations are most likely to occur in the development of lung cancer. In addition, the models are employed to fit the data of female and male patients separately. The interesting result is that, for female patient data the best fit model contains four mutations while that for male patient data is the three-stage model. Finally, robustness analysis suggests that the decrease of cell net proliferation rates is more effective than the decrease of mutation rates in reducing the lung cancer risk. [ABSTRACT FROM AUTHOR]

This paper discusses efficient simulation methods for stochastic chemical kinetics. Based on the τ-leap and midpoint τ-leap methods of Gillespie [D. T. Gillespie, J. Chem. Phys. 115, 1716 (2001)], binomial random variables are used in these leap methods rather than Poisson random variables. The motivation for this approach is to improve the efficiency of the Poisson leap methods by using larger stepsizes. Unlike Poisson random variables whose range of sample values is from zero to infinity, binomial random variables have a finite range of sample values. This probabilistic property has been used to restrict possible reaction numbers and to avoid negative molecular numbers in stochastic simulations when larger stepsize is used. In this approach a binomial random variable is defined for a single reaction channel in order to keep the reaction number of this channel below the numbers of molecules that undergo this reaction channel. A sampling technique is also designed for the total reaction number of a reactant species that undergoes two or more reaction channels. Samples for the total reaction number are not greater than the molecular number of this species. In addition, probability properties of the binomial random variables provide stepsize conditions for restricting reaction numbers in a chosen time interval. These stepsize conditions are important properties of robust leap control strategies. Numerical results indicate that the proposed binomial leap methods can be applied to a wide range of chemical reaction systems with very good accuracy and significant improvement on efficiency over existing approaches. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we propose an approach of combination of asymptotic and numerical techniques to solve highly oscillatory second-order initial value problems. An asymptotic expansion of the solution is derived in inverse of powers of the oscillatory parameter, which develops on two time scales, a slow time t and a fast time τ = ω t. The truncation with the first few terms of the expansion results in a very effective method of discretizing the highly oscillatory differential equation and becomes more accurate when the oscillatory parameter increases. Numerical examples show that our proposed asymptotic-numerical solver is efficient and accurate for highly oscillatory problems. [ABSTRACT FROM AUTHOR]

Drug resistance is one of the most intractable issues associated with cancer treatment in clinical practice. Mathematical models provide an analytic framework for facilitating the understanding of resistance evolution dynamics and the design of cancer clinical trial. In this paper, we develop an elementary, compartmental mathematical model for absolute drug resistance, focusing on the effects of point mutations in genetic drivers of malignancy. A set of ordinary differential equations (ODEs) is used to describe the dynamics of competing heterogeneous cancer cell populations while taking account of pharmacokinetics. All possible equilibria and their local geometric properties are analyzed, with the result suggests that the system exhibits bistable dynamics. The existence of optimal treatment time is discussed. To identify the critical parameters which influence cellular dynamics, we also perform parameter sensitivity analysis. Finally, numerical simulations are presented to verify the feasibilities of our analytical results and to find that the pre-existence of resistant cell phenotypes contributes more than resistant mutants generated during the treatment phase. [ABSTRACT FROM AUTHOR]

Cancer is a class of diseases caused by the accumulation of gene mutations. All mutated genes constitute a genetic network for cancer progression. It is very helpful for tumor diagnosis and therapy if we know how many mutated genes are needed for human breast cancer. In this article, we investigate the mutation mechanisms of human breast cancer by modeling the data of surveillance, epidemiology, and end results registry. The data are age-specific incidence rates of breast cancer of females in the United States. We set up stochastic multistage models to estimate the age-specific incidence rates by using several coupled ordinary differential equations derived from the Kolmogorov backward equations. Our results suggest that 2–14 mutations in the genome of breast stem cells are required for normal breast stem cells to become a malignant cell, and 3 gene mutations are most likely to occur in the development of female breast cancer. [ABSTRACT FROM AUTHOR]

Environment factors such as radiation play an important role in the incidence of lung cancer. In spite of substantial efforts in experimental study and mathematical modeling, it is still a significant challenge to estimate lung cancer risk from radiation. To address this issue, we propose a stochastic model to investigate the impact of radiation on the development of lung cancer. The proposed three-stage model with clonal expansion is used to match the data of the male and female patients in the Osaka Cancer Registry (OCR) and Life Span Study (LSS) cohort of atomic bomb survivors in Hiroshima and Nagasaki. Our results indicate that the major effect of radiation on the development of lung cancer is to induce gene mutations for both male and female patients. In particular, for male patients, radiation affects the mutation in normal cells and the transformation from premalignant cells to malignant ones. However, radiation for female patients increases the mutation rates of the first two mutations in the stochastic model. The established relationship between parameters and radiation will provide insightful prediction for the lung cancer incidence in the radiation exposure. [ABSTRACT FROM AUTHOR]

Stochastic differential equations (SDEs) are a powerful tool to model fluctuations and uncertainty in complex systems. Although numerical methods have been designed to simulate SDEs effectively, it is still problematic when numerical solutions may be negative, but application problems require positive simulations. To address this issue, we propose balanced implicit Patankar–Euler methods to ensure positive simulations of SDEs. Instead of considering the addition of balanced terms to explicit methods in existing balanced methods, we attempt the deletion of possible negative terms from the explicit methods to maintain positivity of numerical simulations. The designed balanced terms include negative-valued drift terms and potential negative diffusion terms. The proposed method successfully addresses the issue of divisions with very small denominators in our recently designed stochastic Patankar method. Stability analysis shows that the balanced implicit Patankar–Euler method has much better stability properties than our recently designed composite Patankar–Euler method. Four SDE systems are used to examine the effectiveness, accuracy, and convergence properties of balanced implicit Patankar–Euler methods. Numerical results suggest that the proposed balanced implicit Patankar–Euler method is an effective and efficient approach to ensure positive simulations when any appropriate stepsize is used in simulating SDEs of biological regulatory systems. [ABSTRACT FROM AUTHOR]

The fast increase of foreign exchange reserve in developing countries has raised a number of important financial questions in recent years. The analysis of the optimal scale of the foreign exchange reserve can provide important indicator to measure the strength and stability of country’s financial standing. In this work we propose a cost-profit model and use the financial data during 2000 to 2008 to analyze the optimal scale of China’s foreign exchange reserve. We identify a number of financial factors to measure the cost and profit of holding the reserves. Our prediction suggested that China’s foreign exchange reserves were still within the moderate range in 1999–2001. However, during 2002–2008 the foreign exchange reserve began to exceed the appropriate scale, and this upward trend was accelerated each year. [ABSTRACT FROM AUTHOR]

Stochastic differential equations (SDE) are a powerful tool to model biological regulatory processes with intrinsic and extrinsic noise. However, numerical simulations of SDE models may be problematic if the values of noise terms are negative and large, which is not realistic for biological systems since the molecular copy numbers or protein concentrations should be non-negative. To address this issue, we propose the composite Patankar-Euler methods to obtain positive simulations of SDE models. A SDE model is separated into three parts, namely, the positive-valued drift terms, negative-valued drift terms, and diffusion terms. We first propose the deterministic Patankar-Euler method to avoid negative solutions generated from the negative-valued drift terms. The stochastic Patankar-Euler method is designed to avoid negative solutions generated from both the negative-valued drift terms and diffusion terms. These Patankar-Euler methods have the strong convergence order of a half. The composite Patankar-Euler methods are the combinations of the explicit Euler method, deterministic Patankar-Euler method, and stochastic Patankar-Euler method. Three SDE system models are used to examine the effectiveness, accuracy, and convergence properties of the composite Patankar-Euler methods. Numerical results suggest that the composite Patankar-Euler methods are effective methods to ensure positive simulations when any appropriate stepsize is used. [ABSTRACT FROM AUTHOR]

Microarray expression profiles are inherently noisy and many different sources of variation exist in microarray experiments. It is still a significant challenge to develop stochastic models to realize noise in microarray expression profiles, which has profound influence on the reverse engineering of genetic regulation. Using the target genes of the tumour suppressor gene p53 as the test problem, we developed stochastic differential equation models and established the relationship between the noise strength of stochastic models and parameters of an error model for describing the distribution of the microarray measurements. Numerical results indicate that the simulated variance from stochastic models with a stochastic degradation process can be represented by a monomial in terms of the hybridization intensity and the order of the monomial depends on the type of stochastic process. The developed stochastic models with multiple stochastic processes generated simulations whose variance is consistent with the prediction of the error model. This work also established a general method to develop stochastic models from experimental information. [Copyright &y& Elsevier]

Abstract: Time delay is an important aspect in the modelling of genetic regulation due to slow biochemical reactions such as gene transcription and translation, and protein diffusion between the cytosol and nucleus. In this paper we introduce a general mathematical formalism via stochastic delay differential equations for describing time delays in genetic regulatory networks. Based on recent developments with the delay stochastic simulation algorithm, the delay chemical master equation and the delay reaction rate equation are developed for describing biological reactions with time delay, which leads to stochastic delay differential equations derived from the Langevin approach. Two simple genetic regulatory networks are used to study the impact of intrinsic noise on the system dynamics where there are delays. [Copyright &y& Elsevier]

Summary: The Raf-MEK-ERK MAP kinase cascade transmits signals from activated receptors into the cell to regulate proliferation and differentiation. The cascade is controlled by the Ras GTPase, which recruits Raf from the cytosol to the plasma membrane for activation. In turn, MEK, ERK, and scaffold proteins translocate to the plasma membrane for activation. Here, we examine the input-output properties of the Raf-MEK-ERK MAP kinase module in mammalian cells activated in different cellular contexts. We show that the MAP kinase module operates as a molecular switch in vivo but that the input sensitivity of the module is determined by subcellular location. Signal output from the module is sensitive to low-level input only when it is activated at the plasma membrane. This is because the threshold for activation is low at the plasma membrane, whereas the threshold for activation is high in the cytosol. Thus, the circuit configuration of the module at the plasma membrane generates maximal outputs from low-level analog inputs, allowing cells to process and respond appropriately to physiological stimuli. These results reveal the engineering logic behind the recruitment of elements of the module from the cytosol to the membrane for activation. [Copyright &y& Elsevier]

In this paper we give an overview of some very recent work, as well as presenting a new approach, on the stochastic simulation of multi-scaled systems involving chemical reactions. In many biological systems (such as genetic regulation and cellular dynamics) there is a mix between small numbers of key regulatory proteins, and medium and large numbers of molecules. In addition, it is important to be able to follow the trajectories of individual molecules by taking proper account of the randomness inherent in such a system. We describe different types of simulation techniques (including the stochastic simulation algorithm, Poisson Runge–Kutta methods and the balanced Euler method) for treating simulations in the three different reaction regimes: slow, medium and fast. We then review some recent techniques on the treatment of coupled slow and fast reactions for stochastic chemical kinetics and present a new approach which couples the three regimes mentioned above. We then apply this approach to a biologically inspired problem involving the expression and activity of LacZ and LacY proteins in E. coli, and conclude with a discussion on the significance of this work. [Copyright &y& Elsevier]

Bistability and switching are two important aspects of the genetic regulatory network of λ phage. Positive and negative feedbacks are key regulatory mechanisms in this network. By the introduction of threshold values, the developmental pathway of λ phage is divided into different stages. If the protein level reaches a threshold value, positive or negative feedback will be effective and regulate the process of development. Using this regulatory mechanism, we present a quantitative model to realize bistability and switching of λ phage based on experimental data. This model gives descriptions of decisive mechanisms for different pathways in induction. A stochastic model is also introduced for describing statistical properties of switching in induction. A stochastic degradation rate is used to represent intrinsic noise in induction for switching the system from the lysogenic pathway to the lysis pathway. The approach in this paper represents an attempt to describe the regulatory mechanism in genetic regulatory network under the influence of intrinsic noise in the framework of continuous models. [Copyright &y& Elsevier]

Cancer diseases lead to the second-highest death rate all over the world. For treating tumors, one of the most common schemes is chemotherapy, which can decrease the tumor size and control the progression of cancer diseases. To better understand the mechanisms of chemotherapy, we developed a mathematical model of tumor growth under chemotherapy. This model includes both immune system response and drug therapy. We characterize the symmetrical properties and dynamics of this differential equation model by finding the equilibrium points and exploring the stability and symmetry properties in a range of model parameters. Sensitivity analyses suggest that the chemotherapy drug-induced tumor mortality rate and the drug decay rate contribute significantly to the determination of treatment outcomes. Numerical simulations highlight the importance of CTL activation in tumor chemotherapy. [ABSTRACT FROM AUTHOR]

Although multistability is an important dynamic property of a wide range of complex systems, it is still a challenge to develop mathematical models for realising high order multistability using realistic regulatory mechanisms. To address this issue, we propose a robust method to develop multistable mathematical models by embedding bistable models together. Using the GATA1-GATA2-PU.1 module in hematopoiesis as the test system, we first develop a tristable model based on two bistable models without any high cooperative coefficients, and then modify the tristable model based on experimentally determined mechanisms. The modified model successfully realises four stable steady states and accurately reflects a recent experimental observation showing four transcriptional states. In addition, we develop a stochastic model, and stochastic simulations successfully realise the experimental observations in single cells. These results suggest that the proposed method is a general approach to develop mathematical models for realising multistability and heterogeneity in complex systems. [ABSTRACT FROM AUTHOR]

Tumor immune escape refers to the inability of the immune system to clear tumor cells, which is one of the major obstacles in designing effective treatment schemes for cancer diseases. Although clinical studies have led to promising treatment outcomes, it is imperative to design theoretical models to investigate the long-term treatment effects. In this paper, we develop a mathematical model to study the interactions among tumor cells, immune escape tumor cells, and T lymphocyte. The chimeric antigen receptor (CAR) T-cell therapy is also described by the mathematical model. Bifurcation analysis shows that there exists backward bifurcation and saddle-node bifurcation when the immune intensity is used as the bifurcation parameter. The proposed model also exhibits bistability when its parameters are located between the saddle-node threshold and backward bifurcation threshold. Sensitivity analysis is performed to illustrate the effects of different mechanisms on the backward bifurcation threshold and basic immune reproduction number. Simulation studies confirm the bifurcation analysis results and predict various types of treatment outcomes using different CAR T-cell therapy strengths. Analysis and simulation results show that the immune intensity can be used to control the tumor size, but it has no effect on the control of the immune escape tumor size. The introduction of the CAR T-cell therapy will reduce the immune escape tumor size and the treatment effect depends on the CAR T-cell therapy strength. [ABSTRACT FROM AUTHOR]

One of the advantages of stochastic differential equations (SDE) is that they can follow a variety of different trends so that they can establish complex dynamic systems in the economic and financial fields. Although some estimation methods have been proposed to identify the unknown parameters in virtue of the results in the SDE model to speed up the process, these solutions only focus on using explicit approach to solve SDEs, and therefore they are not reliable to deal with data source merged being large and varied. Thus, this study makes progress in creating a new implicit way to fill in the gaps of accurately calibrating the unknown parameters in the SDE model. Essentially, the primary goal of the article is to generate rigid SDE simulation. Meanwhile, the particle swarm optimization method serves a purpose to search and simultaneously obtain the optimal estimation of the model unknown parameters in the complicated experiment of parameter space in an effective way. Finally, in an interest rate term structure model, it is verified that the method effectively deals with parameter estimation in the SDE model. [ABSTRACT FROM AUTHOR]

Point prediction has been used to predict air pollutant concentrations in recent years. However, it is still a challenge to characterize the time series data of pollutant concentrations in the presence of high volatility and uncertainty. Since interval prediction can quantity this uncertainty and provide more information than point prediction, we propose an improved interval prediction model based on lower upper bound estimation (LUBE) to construct the prediction intervals (PIs) of PM2.5 concentrations. First, we decompose the original time series into a trend term and a fluctuation term. Then, the trend term with regularity is analyzed by point prediction, while the fluctuation term with uncertainty is studied by LUBE interval prediction. To improve the efficiency and stabilize the randomness in the existing LUBE, we propose a new method based on change point detection and interval perturbation-based adjustment strategy (IPAS). IPAS is used to replace the optimization algorithm in LUBE for improving efficiency. Meanwhile, change point detection is introduced to optimize the initialized parameters in LUBE. In addition, since PM2.5 concentration is influenced by various factors, partial autocorrelation function and maximal information coefficient are applied to select the optimal input features from meteorological and other air pollution factors associated with PM2.5 concentrations. Moreover, we ensemble the prediction results of the trend term and fluctuation term to obtain the ultimate PIs. To evaluate the effectiveness and efficiency of our proposed model, the daily PM2.5 concentration data in Wuhan, China, are analyzed in the empirical study. Comparison results and ablation study clearly indicate that our proposed model has better comprehensive performance than classical models and benchmark models. The proposed new method can provide high-quality PIs and achieve better stability. [ABSTRACT FROM AUTHOR]

Stock correlation networks use stock price data to explore the relationship between different stocks listed in the stock market. Currently this relationship is dominantly measured by the Pearson correlation coefficient. However, financial data suggest that nonlinear relationships may exist in the stock prices of different shares. To address this issue, this work uses mutual information to characterize the nonlinear relationship between stocks. Using 280 stocks traded at the Shanghai Stocks Exchange in China during the period of 2014-2016, we first compare the effectiveness of the correlation coefficient and mutual information for measuring stock relationships. Based on these two measures, we then develop two stock networks using the Minimum Spanning Tree method and study the topological properties of these networks, including degree, path length and the power-law distribution. The relationship network based on mutual information has a better distribution of the degree and larger value of the power-law distribution than those using the correlation coefficient. Numerical results show that mutual information is a more effective approach than the correlation coefficient to measure the stock relationship in a stock market that may undergo large fluctuations of stock prices. [ABSTRACT FROM AUTHOR]

The paper is concerned with stability for second-order stochastic neutral partial functional systems subject to infinite delays and impulses. Some sufficient conditions ensuring pth moment exponential stability of the second-order stochastic systems are given by gaining a new integral inequality with impulses. Some earlier results are generalized and improved. [ABSTRACT FROM AUTHOR]

The rapid progress in biological experimental technologies has generated a huge amount of experimental data to investigate complex regulatory mechanisms. Various mathematical models have been proposed to simulate the dynamic properties of molecular processes using the experimental data. However, it is still difficult to estimate unknown parameters in mathematical models for the dynamics in different cells due to the high demand for computing power. In this work, we propose a population statistical inference algorithm to improve the computing efficiency. In the first step, this algorithm clusters single cells into a number of groups based on the distances between each pair of cells. In each cluster, we then infer the parameters of the mathematical model for the first cell. We propose an adaptive approach that uses the inferred parameter values of the first cell to formulate the prior distribution and acceptance criteria of the following cells. Three regulatory network models were used to examine the efficiency and effectiveness of the designed algorithm. The computational results show that the new method reduces the computational time significantly and provides an effective algorithm to infer the parameters of regulatory networks in a large number of cells. [ABSTRACT FROM AUTHOR]

Breast cancer stem cells (BCSCs) with the ability to self-renew and differentiate have been identified in primary breast cancer tissues and cell lines. The BCSCs are often resistant to traditional radiation and/or chemotherapies. Previous studies have also shown that successful therapy must eradicate cancer stem cells. The purpose of this paper is to develop a mathematical model with self-feedback mechanism to illustrate the issues regarding the difficulties of absolutely eliminating a breast cancer. In addition, we introduce the mechanism of the epithelial-mesenchymal transition (EMT) to investigate the influence of EMT on the effects of breast cancer growth and treatment. Results indicate that the EMT mechanism facilitates the growth of breast cancer and makes breast cancer more difficult to be cured. Therefore, targeting the signals involved in EMT can halt tumor progression in breast cancer. Finally, we apply the experimental data to carry out numerical simulations and validate our theoretical conclusions. [ABSTRACT FROM AUTHOR]

Cancer is one of the leading diseases for human mortality. Although substantial research works have been conducted to investigate the initiation and progression of cancer disease, it is still an active debate regarding the function of mutations conferring a clone advantage and the importance of mutator phenotypes caused by the mutation of stability genes. To address this issue further, we develop a mathematical model based on the incidence data of non-small cell lung cancer and small cell lung cancer from the Surveillance Epidemiology and End Results registry in the USA. The key biological parameters have been analyzed to investigate the potential effective measures for inhibiting the risk of lung cancer. Although the first event is the gene mutation that leads to clonal expansion of cells for lung cancer, the simulation results show that the clonal advantage of cancer cells alone is insufficient to cause tumorigenesis. Our analysis suggests that mutations in genes that keep genetic stability are critical in the development of lung cancer. This implies that mutator phenotype is an important indicator for the diagnosis of lung cancer, which can enable early detection and treatment to reduce the risk of lung cancer effectively. Furthermore, the parameter analysis indicates that it would be highly effective to control the risk of lung cancer by inhibiting the transformation rate from the normal cells to mutated cells and the clonal expansion of cells with fewer gene mutations. [ABSTRACT FROM AUTHOR]

The correlation-based network is a powerful tool to reveal the influential mechanisms and relations in stock markets. However, current methods for developing network models are dominantly based on the pairwise relationship of positive correlations. This work proposes a new approach for developing stock relationship networks by using the linear relationship model with LASSO to explore negative correlations under a systemic framework. The developed model not only preserves positive links with statistical significance but also includes link directions and negative correlations. We also introduce blends cliques with the balance theory to investigate the consistency properties of the developed networks. The ASX 200 stock data with 194 stocks are applied to evaluate the effectiveness of our proposed method. Results suggest that the developed networks not only are highly consistent with the correlation coefficient in terms of positive or negative correlations but also provide influence directions in stock markets. [ABSTRACT FROM AUTHOR]

One of the key challenges in systems biology and molecular sciences is how to infer regulatory relationships between genes and proteins using high-throughout omics datasets. Although a wide range of methods have been designed to reverse engineer the regulatory networks, recent studies show that the inferred network may depend on the variable order in the dataset. In this work, we develop a new algorithm, called the statistical path-consistency algorithm (SPCA), to solve the problem of the dependence of variable order. This method generates a number of different variable orders using random samples, and then infers a network by using the path-consistent algorithm based on each variable order. We propose measures to determine the edge weights using the corresponding edge weights in the inferred networks, and choose the edges with the largest weights as the putative regulations between genes or proteins. The developed method is rigorously assessed by the six benchmark networks in DREAM challenges, the mitogen-activated protein (MAP) kinase pathway, and a cancer-specific gene regulatory network. The inferred networks are compared with those obtained by using two up-to-date inference methods. The accuracy of the inferred networks shows that the developed method is effective for discovering molecular regulatory systems. [ABSTRACT FROM AUTHOR]

The advances of systems biology have raised a large number of mathematical models for exploring the dynamic property of biological systems. A challenging issue in mathematical modeling is how to study the influence of parameter variation on system property. Robustness and sensitivity are two major measurements to describe the dynamic property of a system against the variation of model parameters. For stochastic models of discrete chemical reaction systems, although these two properties have been studied separately, no work has been done so far to investigate these two properties together. In this work, we propose an integrated framework to study these two properties for a biological system simultaneously. We also consider a stochastic model with intrinsic noise for the Nanog gene network based on a published model that studies extrinsic noise only. For the stochastic model of Nanog gene network, we identify key coefficients that have more influence on the network dynamics than the others through sensitivity analysis. In addition, robustness analysis suggests that the model parameters can be classified into four types regarding the bistability property of Nanog expression levels. Numerical results suggest that the proposed framework is an efficient approach to study the sensitivity and robustness properties of biological network models. [ABSTRACT FROM AUTHOR]

Background: Mathematical modeling is an important tool in systems biology to study the dynamic property of complex biological systems. However, one of the major challenges in systems biology is how to infer unknown parameters in mathematical models based on the experimental data sets, in particular, when the data are sparse and the regulatory network is stochastic. Results: To address this issue, this work proposed a new algorithm to estimate parameters in stochastic models using simulated likelihood density in the framework of approximate Bayesian computation. Two stochastic models were used to demonstrate the efficiency and effectiveness of the proposed method. In addition, we designed another algorithm based on a novel objective function to measure the accuracy of stochastic simulations. Conclusions: Simulation results suggest that the usage of simulated likelihood density improves the accuracy of estimates substantially. When the error is measured at each observation time point individually, the estimated parameters have better accuracy than those obtained by a published method in which the error is measured using simulations over the entire observation time period. [ABSTRACT FROM AUTHOR]

This work focuses on gene regulatory networks driven by intrinsic noise with two-time scales. It uses a stochastic averaging approach for these systems to reduce complexity. Comparing with the traditional quasi-steady-state hypothesis (QSSH), our approach uses stochastic averaging principle to treat the intrinsic noise coming from both the fast-changing variables and the slow-changing variables, which yields a more precise description of the underlying systems. To provide further insight, this paper also investigates a prototypical two-component activator-repressor genetic circuit model as an example. If all the protein productions were linear, these two methods would yield the same reduction result. However, if one of the protein productions is nonlinear, the stochastic averaging principle leads to a different reduction result from that of the traditional QSSH. [ABSTRACT FROM AUTHOR]

Recent research indicates that quiescent tumor cells are significantly less radiosensitive with a greater repair capacity than proliferative cells. In order to better predict patient-specific responses to radiotherapy, we develop a mathematical model with treatment terms to describe dynamical behaviors of tumor growth. The global stabilities of the tumor-free equilibrium, the tumor-present equilibrium and the corresponding sufficient criteria are obtained. In addition, we simulate volumetric imaging data from 12 head-and-neck cancer patients and estimate the patient-specific responses to radiotherapy. Results indicate that radiosensitivity of proliferative cells is a critical factor that determines a successful radiotherapy. By comparison with previous simulation results, we find that the model presented in this paper is more suitable to describe the radiotherapy procedure of head-and-neck cancer. Finally, we discuss the influences of different radiotherapy strategies on therapeutic effect. The results show that treatment strategies with large dose or short treatment cycle can obtain better treatment effect. [ABSTRACT FROM AUTHOR]

This work studies stability and stochastic stabilization of numerical solutions of a class of regime-switching jump diffusion systems. These systems have a wide range of applications in communication systems, flexible manufacturing and production planning, financial engineering and economics because they involve three classes of stochastic factors: white noise, Poisson jump and Markovian switching. This paper focuses on the stability of numerical solutions of the switching jump diffusion systems and examines the conditions under which the Euler–Maruyama (EM) and the backward EM may share the stability of the exact solution. These conditions show that all these three classes of stochastic factors may serve as stabilizing factors and play positive roles for the stability property of both exact and numerical solutions. [ABSTRACT FROM PUBLISHER]

The rapid development of the digital economy is a powerful driving force to promote high-quality economic growth all over the world. Although a number of studies have been conducted to investigate the development of the digital economy in China, these studies pay little attention to the spatial linkages between the 30 provinces in China and the developmental differences between northern and southern China. Using Chinese digital economic data from 2004 to 2019, we propose an index system to measure the developmental levels of the digital economy and obtain the annual developmental levels of these provinces by using the factor analysis method. We analyze the regional differences of developmental levels by using the Theil index and kernel density estimation method. More importantly, the network method is used to analyze the correlations between the developmental levels of the digital economy in all provinces of China. By decomposing regional differences, our study shows that polarized and uncoordinated development is prominent. The development level of the digital economy in the southern region is higher than that in the northern region. In terms of regional correlations, the network study suggests that there are beneficial and spillover effects of the digital economy development between provinces. Based on the analysis results, we propose policies for improving the development of the digital economy in China. [ABSTRACT FROM AUTHOR]

Several algorithms have been proposed to filter information on a complete graph of correlations across stocks to build a stock-correlation network. Among them the planar maximally filtered graph (PMFG) algorithm uses 3 n − 6 edges to build a graph whose features include high frequency of small cliques and good clustering of stocks. We propose a new algorithm which we call proportional degree (PD) to filter information on the complete graph of similarities between stocks. Our results show that the PD algorithm produces a network showing better homogeneity with respect to cliques, as compared to economic sectoral classification than its PMFG counterpart regardless of the similarity measure used—the Pearson correlation coefficient or normalised mutual information (NMI). We also show that the partition of the PD network obtained through normalised spectral clustering (NSC) agrees better with the NSC of the complete graph than the corresponding one obtained from PMFG. Finally, we show that the clusters in the PD network are more robust with respect to the removal of random sets of edges than those in the PMFG network. • Cliques homogeneity is higher in PD than PMFG as to stock sectors. • NMI and correlation coefficient result in roughly the same cliques homogeneity. • PD demonstrates a better clustering compared to PMFG. • PD clustering is more robust than that of PMFG after edge removal. [ABSTRACT FROM AUTHOR]

Complex network is a powerful tool to discover important information from various types of big data. Although substantial studies have been conducted for the development of stock relation networks, correlation coefficient is dominantly used to measure the relationship between stock pairs. Information theory is much less discussed for this important topic, though mutual information is able to measure nonlinear pairwise relationship. In this work we propose to use part mutual information for developing stock networks. The path-consistency algorithm is used to filter out redundant relationships. Using the Australian stock market data, we develop four stock relation networks using different orders of part mutual information. Compared with the widely used planar maximally filtered graph (PMFG), we can generate networks with cliques of large size. In addition, the large cliques show consistency with the structure of industrial sectors. We also analyze the connectivity and degree distributions of the generated networks. Analysis results suggest that the proposed method is an effective approach to develop stock relation networks using information theory. [ABSTRACT FROM AUTHOR]

In December 2019, a novel coronavirus, SARS-COV-2, was identified among patients in Wuhan, China. Two strict control measures, i.e., putting Wuhan on lockdown and taking strict quarantine rule, were carried out to contain the spread of COVID-19. Based on the different control measures, we divided the transmission process of COVID-19 into three stages. An SEIHR model was established to describe the transmission dynamics and was applied to fit the published data on the confirmed cases of Wuhan city from December 31, 2019 to March 25, 2020 to deduce the time when the first patient with COVID-19 appeared. The basic reproduction number was estimated in the first stage to demonstrate the number of secondary infectious cases generated by an average infectious case in the absence of policy intervention. The effective reproduction numbers in second and third stages were estimated to evaluate the effects of the two strict control measures. In addition, sensitivity analysis of the reproduction number according to model parameters was executed to demonstrate the effect of the control measures for containing the spread of COVID-19. Finally, the numerical calculation method was applied to investigate the influence of the different control measures on the spread of COVID-19. The results indicated that following the strict quarantine rule was very effective, and reducing the effective contact rates and improving the diagnosis rate were crucial in reducing the effective reproduction number, and taking control measures as soon as possible can effectively contain a larger outbreak of COVID-19. But a bigger challenge for us to contain the spread of COVID-19 was the transmission from the asymptomatic carriers, which required to raising the public awareness of self-protection and keeping a good physical protection. [ABSTRACT FROM AUTHOR]

Genomic instability plays a significant role in lung cancer. Although substantial research has been conducted using both clinical and theoretical studies, it is still a hotly debated issue to whether genomic instability is necessary or whether genomic instability precedes oncogenes activation and tumor suppressor genes inactivation for lung cancer. In response to this issue, we come up with a mathematical model incorporating effects of genomic instability to investigate the genomic instability pathway of human lung cancer. The presented model are applied to match the incidence rate data of lung cancer from the Life Span Study cohort of the atomic bomb survivors in Nagasaki and Hiroshima and the Surveillance Epidemiology and End Results registry in the United States. Model results suggest that genomic instability is necessary in the tumorigenesis of lung cancer, and genomic instability has no significant impact on the net proliferation rate of cells by statistical criteria. By comparing the results of the LSS data to those of the SEER data, we conclude that the genomic instability pathway exhibits a sensitivity to radiation exposure, more intensive in male patients. [ABSTRACT FROM AUTHOR]

Single cell technology is a powerful tool to reveal intercellular heterogeneity and discover cellular developmental processes. When analyzing the complexity of cellular dynamics and variability, it is important to construct a pseudo-time trajectory using single-cell expression data to reflect the process of cellular development. Although a number of computational and statistical methods have been developed recently for single-cell analysis, more effective and efficient methods are still strongly needed. In this work we propose a new method named SCOUT for the inference of single-cell pseudo-time ordering with bifurcation trajectories. We first propose to use the fixed-radius near neighbors algorithms based on cell densities to find landmarks to represent the cell states, and employ the minimum spanning tree (MST) to determine the developmental branches. We then propose to use the projection of Apollonian circle or a weighted distance to determine the pseudo-time trajectories of single cells. The proposed algorithm is applied to one synthetic and two realistic single-cell datasets (including single-branching and multi-branching trajectories) and the cellular developmental dynamics is recovered successfully. Compared with other popular methods, numerical results show that our proposed method is able to generate more robust and accurate pseudo-time trajectories. The code of the method is implemented in Python and available at https://github.com/statway/SCOUT. [ABSTRACT FROM AUTHOR]

This paper aims at investigating how the media coverage and smoking cessation treatment should be implemented, for a certain period, to reduce the numbers of smokers and patients caused by smoking while minimizing the total cost. To this end, we first propose a new mathematical model without any control strategies to investigate the dynamic behaviors of smoking. Furthermore, we calculate the basic reproduction number R0 and discuss the global asymptotic stabilities of the equilibria. Then, from the estimated parameter values, we know that the basic reproduction number R0 is more than 1, which reveals that smoking is one of the enduring problems of the society. Hence, we introduce two control measures (media coverage and smoking cessation treatment) into the model. Finally, in order to investigate their effects in smoking control and provide an analytical method for the strategic decision-makers, we apply a concrete example to calculate the incremental cost-effectiveness ratios and analyze the cost-effectiveness of all possible combinations of the two control measures. The results indicate that the combination of media coverage and smoking cessation treatment is the most cost-effective strategy for tobacco control. [ABSTRACT FROM AUTHOR]

Investigating the dynamics of genetic regulatory networks through high throughput experimental data, such as microarray gene expression profiles, is a very important but challenging task. One of the major hindrances in building detailed mathematical models for genetic regulation is the large number of unknown model parameters. To tackle this challenge, a new integrated method is proposed by combining a top-down approach and a bottom-up approach. First, the top-down approach uses probabilistic graphical models to predict the network structure of DNA repair pathway that is regulated by the p53 protein. Two networks are predicted, namely a network of eight genes with eight inferred interactions and an extended network of 21 genes with 17 interactions. Then, the bottom-up approach using differential equation models is developed to study the detailed genetic regulations based on either a fully connected regulatory network or a gene network obtained by the top-down approach. Model simulation error, parameter identifiability and robustness property are used as criteria to select the optimal network. Simulation results together with permutation tests of input gene network structures indicate that the prediction accuracy and robustness property of the two predicted networks using the top-down approach are better than those of the corresponding fully connected networks. In particular, the proposed approach reduces computational cost significantly for inferring model parameters. Overall, the new integrated method is a promising approach for investigating the dynamics of genetic regulation. [ABSTRACT FROM AUTHOR]

The study of resilience for high-dimensional systems is a challenging problem in physical sciences. Although a generic dimensional reduction method has been proposed to study the resilience of large-scale networks, an important yet unsolved question is how different types of regulation affect network resilience. Here we propose a new method to reduce the size of a large-scale regulatory network to the number of regulation types in the system. For each type of regulation, a symbolic variable is introduced to represent the function of that regulation in determining the resilience of the high-dimensional network. Using the genetic networks in Escherichia coli and Saccharomyces cerevisiae as the test systems, we examine how positive and negative regulation affect the resilience of these systems. Analytical and numerical studies suggest that the reduction of positive regulation deteriorates network resilience, while the decline of negative regulation enhances the resilience property. More importantly, we show that there is a trade-off between network efficiency and resilience, which is supported by the balance of positive and negative regulation. The proposed method provides a general framework to evaluate the key role of different regulatory mechanisms in determining the resilience of high-dimensional networks. • New method to evaluate resilience of networks with different types of regulation. • Introduction of variables to represent functions of different types of regulation. • Examine effects of positive and negative regulation on resilience of gene network. • Trade-off between network efficiency and resilience via balance of regulations. [ABSTRACT FROM AUTHOR]

The development of stock relationship networks is an important topic to explore the potential connections between different stocks. The methods based on the threshold and correlation relationship have been designed in recent years to construct networks by selecting the highly correlated links. However, if a single threshold value is used, one of the major challenges in these methods is the balance between the degree of stocks and the connectivity of the generated network. To address this issue, we propose a new method to make proper selections of links and maintain the connectivity of established networks. Instead of using a single threshold value for the whole network, our proposed approach selects a threshold value for each stock using the maximum likelihood estimation. The innovation of our method is to apply different distribution functions to the weak and strong correlations separately. Using the dataset from the Chinese Shanghai security market, we develop the stock correlation networks and analyze the topological properties of established networks, including the degree distribution, clustering coefficient and clique. Our results suggest that the proposed method is able to provide better insights into the characteristics of the stock market. • A new method to select essential edges and maintain connectivity of stock networks. • Use different threshold values for choosing the edges connections of different stocks. • Propose to use multiple distributions in maximum likelihood to select threshold values. • Use the Chinese Shanghai security market data of 151 stocks to develop stock network. [ABSTRACT FROM AUTHOR]