Office: University Hall 2771
Dr. Ma's interests are in applied mathematics, especially in biomathematics. Dr. Ma received her Ph.D. in applied mathematics with a minor in statistics from Pennsylvania State University in 2011 and her B.S. from the University of Science and Technology of China in 2006. She joined the LMU faculty in 2011.
The Pennsylvania State University: Ph.D., Applied Mathematics 2011
The Pennsylvania State University: M.A., Mathematics 2009
University of Science and Technology of China: B.Sc., Mathmatics and Applied Mathematics 2006
Areas of Expertise (13)
Industry Expertise (2)
MATH 120 PreCalculus
Fall 2020, Summer 2020, Fall 2011
MATH 122 Calculus I for Life Science
Spring 2021, Spring 2020, Spring 2019, Spring 2018, Spring 2017, Fall 2016, Spring 2016, Fall 2015, Spring 2014, Fall 2013, Fall 2012, Spring 2012
MATH 131 Calculus I
Summer 2019, Fall 2017, Summer 2012
MATH 234 Multivariable Calculus
MATH 245 Ordinary Differential Equations
Spring 2021, Fall 2019, Spring 2018, Spring 2013
MATH 321 Real Variables
Fall 2016, Fall 2015
MATH 355 Methods of Applied Mathematics
Spring 2020, Fall 2018, Summer 2014(Bonn, Germany)
MATH 357 Complex Variables
Fall 2019, Fall 2018
MATH 360 Introduction to Probability and Statistics
Fall 2020, Spring 2017
MATH 398 Real Variables I ( four unit Pilot)
Fall, 2016, Fall 2015
MATH/BIOL/HHSC 398 Ecology of Homelessness
MATH 495 Mathematical Modeling
Spring 2019, Spring 2014
MATH 499 Introduction to Numerical Analysis
MATH 562 Numerical Analysis
Application of population dynamics to study heterotypic cell aggregations in the near-wall region of a shear flowCellular and Molecular Bioengineering
Y. Ma, J. Wang, S. Liang, C. Dong and Q. Du
Our research focused on the polymorphonuclear neutrophils (PMNs) tethering to the vascular endothelial cells (EC) and the subsequent melanoma cell emboli formation in a shear flow, an important process of tumor cell extravasation from the circulation during metastasis. We applied population balance model based on Smoluchowski coagulation equation to study the heterotypic aggregation between PMNs and melanoma cells in the near-wall region of an in vitro parallel-plate flow chamber, which simulates in vivo cell-substrate adhesion from the vasculatures by combining mathematical modeling and numerical simulations with experimental observations. To the best of our knowledge, a multiscale near-wall aggregation model was developed, for the first time, which incorporated the effects of both cell deformation and general ratios of heterotypic cells on the cell aggregation process. Quantitative agreement was found between numerical predictions and in vitro experiments. ...
Population Dynamics Modeling of Heterotypic Cell Aggregations and Related Parameter Identification ProblemsPh.D. Thesis
Cancer has been one of the leading causes of death around the world for decades. Metastasis, the spread of the tumor cells from the primary site to other locations in the body via the lymphatic system or through the bloodstream, is responsible for most of the cancer deaths. Massive experimental studies have been done in these areas. The work of this thesis brings together the experimental, numerical, and mathematical studies on the step of polymorphonuclear neutrophils (PMNs) tethering to the vascular endothelial cells (EC), and the subsequent melanoma cell emboli formation in a nonlinear shear flow, both of which are important in tumor cell extravasations from the circulation during metastasis.
Injury-Initiated Clot Formation Under Flow: A Mathematical Model with Warfarin TreatmentApplications of Dynamical Systems in Biology and Medicine, The IMA Volumes in Mathematics and its Applications 158
L. de Pillis, E. Graham, K. Hood, Y. Ma, A. Radunskaya and J. Simon
The formation of a thrombus (commonly referred to as a blood clot) can potentially pose a severe health risk to an individual, particularly when a thrombus is large enough to impede blood flow. If an individual is considered to be at risk for forming a thrombus, he/she may be prophylactically treated with anticoagulant medication such as warfarin. When an individual is treated with warfarin, a blood test that measures clotting times must be performed. The test yields a number known as the International Normalized Ratio (INR). The INR test must be performed on an individual on a regular basis (e.g., monthly) to ensure that warfarin’s anticoagulation action is targeted appropriately. In this work, we explore the conditions under which an injury-induced thrombus may form in vivo even when the in vitro test shows the appropriate level of anticoagulation action by warfarin. We extend previous models to describe the in vitro clotting time test, as well as thrombus formation in vivo with warfarin treatments. We present numerical simulations that compare scenarios in which warfarin doses and flow rates are modified within biological ranges. Our results indicate that traditional INR measurements may not accurately reflect in vivo clotting times.
A stochastic model for microbial fermentation process under Gaussian white noise environmentNumerical Algebra, Control and Optimization (NACO)
Y. Wang, L. Wang, Y. Zhao, A. Song, and Y. Ma
In this paper, we propose a stochastic model for the microbial fermentation process under the framework of white noise analysis, where Gaussian white noises are used to model the environmental noises and the specific growth rate is driven by Gaussian white noises. In order to keep the regularity of the terminal time, the adjustment factors are added in the volatility coefficients of the stochastic model. Then we prove some fundamental properties of the stochastic model: the regularity of the terminal time, the existence and uniqueness of a solution and the continuous dependence of the solution on the initial values.
Generalized local and nonlocal master equations for some stochastic processesComputers & Mathematics with Applications
Y. Zhao, J. Wang, Y. Ma, and Q. Du
In this paper, we present a study on generalized local and nonlocal equations for some stochastic processes. By considering the net flux change in a region determined by the transition probability, we derive the master equation to describe the evolution of the probability density function. Some examples, such as classical Fokker–Planck equations, models for Lévy process, and stochastic coagulation equations, are provided as illustrations. A particular application is a consistent derivation of coupled dynamical systems for spatially inhomogeneous stochastic coagulation processes.
A Novel Fractional Microbial Batch Culture Process and Parameter IdentificationDifferential Equations and Dynamical Systems
P. Mu, L. Wang, Y. An, and Y. Ma
This paper considers the microbial batch culture for producing 1,3-propanediol(1,3-PD) via glycerol disproportionation. Due to the nature of the fractional order operations, a novel fractional order model, which is based upon the original ordinary differential dynamic system, is introduced to describe the complex bioprocess in a more accurate manner. Existence and uniqueness of solutions to the novel fractional order system and the continuity of solutions with respect to the parameters are discussed respectively. In addition, a parameter identification problem of the system is presented, and a particle swarm optimization algorithm is constructed to solve it. Finally, the conclusion is drawn by numerical simulations.
Stochastic maximum principle for partial information optimal investment and dividend problem of an insurerJournal of industrial and management optimization
Y. Wang, Y. Zhao, L. Wang, A. Song and Y. Ma
We study an optimal investment and dividend problem of an insurer, where the aggregate insurance claims process is modeled by a pure jump Lévy process. We allow the management of the dividend payment policy and the investment of surplus in a continuous-time financial market, which is composed of a risk free asset and a risky asset. The information available to the insurer is partial information. We generalize this problem as a partial information regular-singular stochastic control problem, where the control variable consists of regular control and singular control. Then maximum principles are established to give sufficient and necessary optimality conditions for the solutions of the regular-singular control problem. Finally we apply the maximum principles to solve the investment and dividend problem of an insurer.
A linear optimal feedback control for producing 1, 3-propanediol via microbial fermentationDiscrete and Continuous Dynamical Systems - Series S
H. Bei, L. Wang, Y. Ma, J. Sun, and L. Zhang
In this paper, we consider a multistage feedback control strategy for the production of 1, 3-propanediol(1, 3-PD) in microbial fermentation. The feedback control strategy is widely used in industry, and to the best of our knowledge, this is the first time it is applied to 1, 3-PD. The feedback control law is assumed to be linear of the concentrations of biomass and glycerol, and the coefficients in the controller are continuous. A multistage feedback control law is obtained by using the control parameterization method on the coefficient functions. Then, the optimal control problem can be transformed into an optimal parameter selection problem. The time horizon is partitioned adaptively. The corresponding gradients are derived, and finally, our numerical results indicate that the strategy is flexible and efficient.
A New Phase-field Approach to Variational Implicit Salvation of Charged Molecules with the Coulomb-field ApproximationCommunications in Mathematical Sciences
Zhao, Y. Ma, H. Sun, B. Li and Q. Du
We construct a new phase-field model for the solvation of charged molecules with a variational implicit solvent. Our phase-field free-energy functional includes the surface energy, solute-solvent van der Waals dispersion energy, and electrostatic interaction energy that is described by the Coulomb-field approximation, all coupled together self-consistently through a phase field. By introducing a new phase-field term in the description of the solute-solvent van der Waals and electrostatic interactions, we can keep the phase-field values closer to those describing the solute and solvent regions, respectively, making it more accurate in the free-energy estimate. We first prove that our phase-field functionals Γ-converge to the corresponding sharp-interface limit. We then develop and implement an efficient and stable numerical method to solve the resulting gradient-flow equation to obtain equilibrium conformations and their associated free energies of the underlying charged molecular system. Our numerical method combines a linear splitting scheme, spectral discretization, and exponential time differencing Runge-Kutta approximations. Applications to the solvation of single ions and a two-plate system demonstrate that our new phase-field implementation improves the previous ones by achieving the localization of the system forces near the solute-solvent interface and maintaining more robustly the desirable hyperbolic tangent profile for even larger interfacial width. This work provides a scheme to resolve the possible unphysical feature of negative values in the phase-field function found in the previous phase-field modeling (cf. H. Sun, et al. J. Chem. Phys., 2015) of charged molecules with the Poisson–Boltzmann equation for the electrostatic interaction.
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