# UMBC Mathematics and Statistics Department

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Item Pretest Estimation for the Common Mean of Several Normal Distributions: In Meta-Analysis Context(MDPI, 2024-9-22) Mphekgwana, Peter M.; Kifle, Yehenew Getachew; Marange, Chioneso S.Show more The estimation of unknown quantities from multiple independent yet non-homogeneous samples has garnered increasing attention in various fields over the past decade. This interest is evidenced by the wide range of applications discussed in recent literature. In this study, we propose a preliminary test estimator for the common mean (𝜇) with unknown and unequal variances. When there exists prior information regarding the population mean with consideration that 𝜇 might be equal to the reference value for the population mean, a hypothesis test can be conducted: H₀ : 𝜇 = 𝜇₀ versus H₁ : 𝜇 ≠ 𝜇₀. The initial sample is used to test H₀, and if H₀ is not rejected, we become more confident in using our prior information (after the test) to estimate 𝜇. However, if H₀ is rejected, the prior information is discarded. Our simulations indicate that the proposed preliminary test estimator significantly decreases the mean squared error (MSE) values compared to unbiased estimators such as the Garybill-Deal (GD) estimator, particularly when 𝜇 closely aligns with the hypothesized mean (𝜇₀). Furthermore, our analysis indicates that the proposed test estimator outperforms the existing method, particularly in cases with minimal sample sizes. We advocate for its adoption to improve the accuracy of common mean estimation. Our findings suggest that through careful application to real meta-analyses, the proposed test estimator shows promising potential.Show more Item Existence and uniqueness of Koopman eigenfunctions near stable equilibria and limit cycles(2022-12-13) Kvalheim, Matthew D.Show more Item Asymptotic stabilizability(2023-06-13) Kvalheim, Matthew D.Show more Item Linearizability of dynamical systems by embeddings(2024-06-01) Kvalheim, Matthew D.Show more Item Relationships Between Necessary Conditions for Feedback Stabilizability(2024-06-05) Kvalheim, Matthew D.Show more The author's extensions of Brockett's and Coron's necessary conditions for stabilizability are shown to be independent in the fiber bundle picture of control, but the latter is shown to be stronger in the vector bundle picture if the state space is orientable and the Cech-Euler characteristic of the set to be stabilized is nonzero.Show more Item Mechanistic insights into condensate formation of human liver-type phosphofructokinase by stochastic modeling approaches(Nature, 2024-08-16) Kang, Hye-Won; Nguyen, Luan; An, Songon; Kyoung, MinjoungShow more Human liver-type phosphofructokinase 1 (PFKL) has been shown to regulate glucose flux as a scaffolder arranging glycolytic and gluconeogenic enzymes into a multienzyme metabolic condensate, the glucosome. However, it has remained elusive of how phase separation of PFKL is governed and initiates glucosome formation in living cells, thus hampering to understand a mechanism of glucosome formation and its functional contribution to human cells. In this work, we developed a stochastic model in silico using the principle of Langevin dynamics to investigate how biological properties of PFKL contribute to the condensate formation. The significance of an intermolecular interaction between PFKLs, an effective concentration of PFKL at a region of interest, and its own self-assembled filaments in formation of PFKL condensates and control of their sizes were demonstrated by molecular dynamics simulation using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). Such biological properties that define intracellular dynamics of PFKL appear to be essential for phase separation of PFKL, which may represent an initiation step for the formation of glucosome condensates. Collectively, our computational study provides mechanistic insights of glucosome formation, particularly an initial stage through the formation of PFKL condensates in living human cells.Show more Item Improving adherence to a daily PrEP regimen is key when considering long-time partnerships(Taylor & Francis, 2024-12-31) Gutowska, S. J.; Hoffman, Kathleen; Gurski, K. F.Show more A population model of HIV that includes susceptible individuals not taking the pre-exposure prophylaxis (PrEP), susceptible individuals taking daily PrEP, and infected individuals is developed for casual partnerships, as well as monogamous and non-monogamous long-term partnerships. Reflecting the reality of prescription availability and usage in the U.S., the PrEP taking susceptible population is a mix of individuals designated by the CDC as high and low risk for acquiring HIV. The rate of infection for non-monogamous long-term partnerships with differential susceptibility is challenging to calculate and requires Markov chain theory to represent the movement between susceptible populations before infection. The parameters associated with PrEP initiation, suspension and adherence impact both the reproduction number of the model and the elasticity indices of the reproduction model. A multi-parameter analysis reveals that increasing adherence has the largest effect on decreasing the number of new infections.Show more Item Developing a Career-Focused, Diverse Mentoring Program for Underrepresented STEM Undergraduates(The University of New Mexico, 2024-06-01) Wayman, Annica; Stolle-McAllister, Kathleen; LaCourse, WilliamShow more The racial and gender composition of the STEM workforce and holders of advanced degrees still has low representation from those traditionally underrepresented groups (URGs) in STEM. Having little representation of URGs in the STEM workforce, especially among academic faculty, perpetuates the issue of STEM students having few, if any, diverse STEM faculty to engage which has been shown to hinder retention in STEM. While involving STEM students from URGs in research mentoring experiences with non-minority faculty mentors addresses this issue to some extent, it also may limit a student’s exposure to STEM careers beyond academic research which may help retain them. Thus, the UMBC STEM BUILD program developed and implemented a career-focused mentoring program that included a broad array of STEM professions from URGs to support career development of 2nd year STEM students.Show more Item Semigroup Methods for Poroelastic Multi-Physics Systems Describing Biological Tissues(2024/01/01) Gurvich, Elena; Webster, Justin T; Mathematics and Statistics; Mathematics, AppliedShow more This thesis presents novel work in the mathematical theory of poroelasticity, which was first phenomenologically developed by Biot and Zenisek during the mid-last century. The theory relates saturated porous structural deformations to fluid pressure changes within, and blossomed through many applications in the geosciences (e.g., seismic and petroleum engineering). At the outset of the 21st century, poroelasticity proved to be a revolutionary incorporation to the biological fields (e.g. biomedical engineering, arterial stents, scaffolding), owing to the poroelastic nature of biological tissues. For the parameters of physical interest, a quasi-static approximation induces dynamics, which can be represented as an implicit evolution. Moreover, compressibility in Biot's equations is a significant consideration. In the incompressible limit, Biot’s model degenerates This dissertation will present a biologically motivated multilayered system, composed of the coupled dynamics of a 3D poroelastic structure, a poroelastic plate, and an incompressible free Stokes flow. We propose two constituent sub-problems, to gain a better understanding of this extremely complex system. First, a complete well-posedness analysis of the poroelastic plate is shown utilizing variational tools. Secondly, Biot-Stokes filtration is proposed with Beavers-Joseph-Saffman coupling conditions on a fixed 2D interface. A semigroup approach is used to bypass the issues with mismatched trace regularities on the interface; thus guaranteeing strong and generalized solutions. Then the existence of weak solutions, including the degenerate case, is provided by argument by density. The most interesting cases are singular limits, which lead to the use of the theory of abstract implicit, degenerate evolutions, of which the appendix supplies a brief overview. Thus, this thesis provides a clear elucidation of strong solutions and the construction of weak solutions for inertial linear Biot-Stokes filtration systems and uniquely for a poroelastic plate, as well as their regularity through associated estimates.Show more Item Disciplinary Differences in STEM Faculty and Student Use of Learning Objectives: Implications for Teaching and Learning(Taylor & Francis, 2024-07-22) Leupen, Sarah; Williams, Tory; Hodges, Linda C.; Ott, Laura E.; Anderson, Eric C.; Cui, Lili; Nanes, Kalman M.; Perks, H. Mark; Wagner, Cynthia R.Show more Using learning objectives to guide course design is often considered an educational best practice, but little research exists that explores how students use them over time and across courses. We surveyed students on their use and perceived value of learning objectives as the semester progressed across four science, technology, engineering, and mathematics (STEM) disciplines, examined students’ ability to match exam questions with learning objectives, and analyzed how their course performance related to these qualities. We also gathered instructors’ information on their implementation of learning objectives in these courses. We identified distinct disciplinary differences both in students’ use and perceived benefit of learning objectives and in instructors’ implementation of them. Students in less quantitatively focused courses, i.e., biology and organic chemistry, reported valuing and using learning objectives more than students in more quantitatively focused math and physics courses. Students’ ability to match learning objectives with exam questions, however, positively correlated with exam score and final course grade in all our study courses. Our results have implications for considering disciplinary practices for use of learning objectives as instructors design and implement courses, educational researchers plan studies, and assessment specialists formulate institutional assessment plans.Show more Item Semistability of switched linear systems with applications to distributed sensor networks: A generating function approach(IEEE, 2012-03-01) Shen, Jinglai; Hu, Jianghai; Hui, QingShow more This paper investigates semistability of discrete-time, switched linear systems under both deterministic and random switching policies. The notion of semistability pertains to a continuum of initial state dependent equilibria and has found wide applications such as consensus problems in multi-agent systems. The main contributions of the paper are three folds. First, we show that exponential semistability on a common equilibrium space is equivalent to output exponential stability of the switched linear system with a suitably defined output, under both arbitrary and random switchings. Further, their convergence rates are shown to be identical. Second, it is shown that output stability and its convergence rates can be efficiently characterized via the recently developed generating function approach. Third, we consider algorithm development and analysis of resource allocation schemes for topologically changing, distributed sensor networks. We formulate an iteration process of such an algorithm as a switched linear system, and characterize its convergence using the obtained semistability results.Show more Item Stabilization of Switched Linear Systems Using Continuous Control Input against Known Adversarial Switching(IEEE, 2018-06) Hu, Jianghai; Shen, Jinglai; Lee, DonghwanShow more The problem of designing continuous control input to stabilize switched linear control systems against adversarial switching is studied. It is assumed that the continuous controller has access to the current switching mode and can be of the form of an ensemble of mode-dependent state feedback controllers. The fastest stabilizing rate under the given information structure is proposed as a quantitative metric of the system's stabilizability, and its bounds are derived using seminorms. Computation algorithms for the stabilizing rate are developed and illustrated through examples.Show more Item Convex regression via penalized splines: A complementarity approach(IEEE, 2012-10-01) Shen, Jinglai; Wang, XiaoShow more Estimation of a convex function is an important shape restricted nonparametric inference problem with broad applications. In this paper, penalized splines (or simply P-splines) are exploited for convex estimation. The paper is devoted to developing an asymptotic theory of a class of P-spline convex estimators using complementarity techniques and asymptotic statistics. Due to the convex constraints, the optimality conditions of P-splines are characterized by nons-mooth complementarity conditions. A critical uniform Lipschitz property is established for optimal spline coefficients. This property yields boundary consistency and uniform stochastic boundedness. Using this property, the P-spline estimator is approximated by a two-step estimator based on the corresponding least squares estimator, and its asymptotic behaviors are obtained using asymptotic statistic techniques.Show more Item Stabilizing switched linear systems under adversarial switching(IEEE, 2015-12) Hu, Jianghai; Lee, Dong-Hwan; Shen, JinglaiShow more The problem of stabilizing discrete-time switched linear control systems using continuous input by the user and against adversarial switching by an adversary is studied. It is assumed that the adversary has the advantage in that at each time it knows the user's decision on the continuous control input but not vice versa. Stabilizability conditions and bounds on the fastest stabilizing rates are derived. Examples are given to illustrate the results.Show more Item Mathematical Models for the Triaxial Attitude Control Testbed(Taylor & Francis, 2010-08-09) Cho, Sangbum; Shen, Jinglai; Mcclamroch, N. HarrisShow more The Triaxial Attitude Control Testbed has been developed as part of a research program at the University of Michigan on multibody rotational dynamics and control. In this paper, equations of motion are derived and presented in various forms. Actuation mechanisms are incorporated into the models; these include fan actuators, reaction wheel actuators and proof mass actuators that are fixed to the triaxial base body. The models also allow incorporation of unactuated auxiliary bodies that are constrained to move relative to the triaxial base body. The models expose the dynamic coupling between the rotational motion of the triaxial base body, the relative or shape motion of the unactuated auxiliary degrees of freedom, and dynamics associated with actuation mechanisms. Many different model simplifications and approximations are developed. Control models for the triaxial attitude control testbed are formulated that reflect specific assumptions.Show more Item ROBUST DYNAMIC INVERSION DESIGN OF MANEUVERABLE FLIGHT COMMAND TRACKING SYSTEMS(Beijing University of Aeronautics & Astronautics, 1998-10-25) Jinglai, Shen; Jinyuan, GaoShow more The design of a maneuverable flight command tracking system using nonlinear dynamic inversion is briefly introduced at first. And then a robust controller to improve the robustness of dynamic inversion is designed using the method of μ analysis and synthesis. The detailed design process and results are presented. Simulations show that the robust dynamic inversion controller yields good results.Show more Item Stability and Stabilization of Relative Equilibria of Dumbbell Bodies in Central Gravity(AIAA, 2005-09) Sanyal, Amit K.; Shen, Jinglai; McClamroch, N. Harris; Bloch, Anthony M.Show more A dumbbell-shaped rigid body can be used to represent certain large spacecraft or asteroids with bimodal mass distributions. Such a dumbbell body is modeled as two identical mass particles connected by a rigid, massless link. Equations of motion for the five degrees of freedom of the dumbbell body in a central gravitational field are obtained. The equations of motion characterize three orbit degrees of freedom, two attitude degrees of freedom, and the coupling between them. The system has a continuous symmetry due to a cyclic variable associated with the angle of right ascension of the dumbbell body. Reduction with respect to this symmetry gives a reduced system with four degrees of freedom. Relative equilibria, corresponding to circular orbits, are obtained from these reduced equations of motion; the stability of these relative equilibria is assessed. It is shown that unstable relative equilibria can be stabilized by suitable attitude feedback control of the dumbbell.Show more Item Linear Complementarity Systems: Zeno States(SIAM, 2005-01) Shen, Jinglai; Pang, Jong-ShiShow more A linear complementarity system (LCS) is a hybrid dynamical system defined by a linear time-invariant ordinary differential equation coupled with a finite-dimensional linear complementarity problem (LCP). The present paper is the first of several papers whose goal is to study some fundamental issues associated with an LCS. Specifically, this paper addresses the issue of Zeno states and the related issue of finite number of mode switches in such a system. The cornerstone of our study is an expansion of a solution trajectory to the LCS near a given state in terms of an observability degree of the state. On the basis of this expansion and an inductive argument, we establish that an LCS satisfying the P-property has no strongly Zeno states. We next extend the analysis for such an LCS to a broader class of problems and provide sufficient conditions for a given state to be weakly non-Zeno. While related mode-switch results have been proved by Brunovsky and Sussmann for more general hybrid systems, our analysis exploits the special structure of the LCS and yields new results for the latter that are of independent interest and complement those by these two and other authors.Show more Item Lyapunov Stability of Complementarity and Extended Systems(SIAM, 2007-01) Camlibel, M. Kanat; Pang, Jong‐Shi; Shen, JinglaiShow more A linear complementarity system (LCS) is a hybrid dynamical system defined by a linear time-invariant ordinary differential equation coupled with a finite-dimensional linear complementarity problem (LCP). The present paper is the first of several papers whose goal is to study some fundamental issues associated with an LCS. Specifically, this paper addresses the issue of Zeno states and the related issue of finite number of mode switches in such a system. The cornerstone of our study is an expansion of a solution trajectory to the LCS near a given state in terms of an observability degree of the state. On the basis of this expansion and an inductive argument, we establish that an LCS satisfying the P-property has no strongly Zeno states. We next extend the analysis for such an LCS to a broader class of problems and provide sufficient conditions for a given state to be weakly non-Zeno. While related mode-switch results have been proved by Brunovsky and Sussmann for more general hybrid systems, our analysis exploits the special structure of the LCS and yields new results for the latter that are of independent interest and complement those by these two and other authors.Show more Item Smoothing splines with varying smoothing parameter(Oxford University Press, 2013-06-08) Wang, Xiao; Du, Pang; Shen, JinglaiShow more This paper considers the development of spatially adaptive smoothing splines for the estimation of a regression function with nonhomogeneous smoothness across the domain. Two challenging issues arising in this context are the evaluation of the equivalent kernel and the determination of a local penalty. The penalty is a function of the design points in order to accommodate local behaviour of the regression function. We show that the spatially adaptive smoothing spline estimator is approximately a kernel estimator, and that the equivalent kernel is spatially dependent. The equivalent kernels for traditional smoothing splines are a special case of this general solution. With the aid of the Green’s function for a two-point boundary value problem, explicit forms of the asymptotic mean and variance are obtained for any interior point. Thus, the optimal roughness penalty function is obtained by approximately minimizing the asymptotic integrated mean squared error. Simulation results and an application illustrate the performance of the proposed estimator.Show more