UMBC Mathematics and Statistics Department
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Item Using Neural Networks to Sanitize Compton Camera Simulated Data through the BRIDE Pipeline for Improving Gamma Imaging in Proton Therapy on the ada Cluster(2024) Chen, Michael O.; Hodge, Julian; Jin, Peter L.; Protz, Ella; Wong, Elizabeth; Obe, Ruth; Shakeri, Ehsan; Cham, Mostafa; Gobbert, Matthias; Barajas, Carlos A.; Jiang, Zhuoran; Sharma, Vijay R.; Ren, Lei; Mossahebi, Sina; Peterson, Stephen W.; Polf, Jerimy C.Precision medicine in cancer treatment increasingly relies on advanced radiotherapies, such as proton beam radiotherapy, to enhance e?cacy of the treatment. When the proton beam in this treatment interacts with patient matter, the excited nuclei may emit prompt gamma ray interactions that can be captured by a Compton camera. The image reconstruction from this captured data faces the issue of mischaracterizing the sequences of incoming scattering events, leading to excessive background noise. To address this problem, several machine learning models such as Feedfoward Neural Networks (FNN) and Recurrent Neural Networks (RNN) were developed in PyTorch to properly characterize the scattering sequences on simulated datasets, including newly-created patient medium data, which were generated by using a pipeline comprised of the GEANT4 and Monte-Carlo Detector E?ects (MCDE) softwares. These models were implemented using the novel 態ig-data REU Integrated Development and Experimentation� (BRIDE) platform, a modular pipeline that streamlines preprocessing, feature engineering, and model development and evaluation on parallelized GPU processors. Hyperparameter studies were done on the novel patient data as well as on water phantom datasets used during previous research. Patient data was more di?cult than water phantom data to classify for both FNN and RNN models. FNN models had higher accuracy on patient medium data but lower accuracy on water phantom data when compared to RNN models. Previous results on several di?erent datasets were reproduced on BRIDE and multiple new models achieved greater performance than in previous research.Item Profile least squares estimation in networks with covariates(2024-12-20) Chandna, Swati; Bagozzi, Benjamin; Chatterjee, SnigdhansuMany real world networks exhibit edge heterogeneity with different pairs of nodes interacting with different intensities. Further, nodes with similar attributes tend to interact more with each other. Thus, in the presence of observed node attributes (covariates), it is of interest to understand the extent to which these covariates explain interactions between pairs of nodes and to suitably estimate the remaining structure due to unobserved factors. For example, in the study of international relations, the extent to which country-pair specific attributes such as the number of material/verbal conflicts and volume of trade explain military alliances between different countries can lead to valuable insights. We study the model where pairwise edge probabilities are given by the sum of a linear edge covariate term and a residual term to model the remaining heterogeneity from unobserved factors. We approach estimation of the model via profile least squares and show how it leads to a simple algorithm to estimate the linear covariate term and the residual structure that is truly latent in the presence of observed covariates. Our framework lends itself naturally to a bootstrap procedure which is used to draw inference on model parameters, such as to determine significance of the homophily parameter or covariates in explaining the underlying network structure. Application to four real network datasets and comparisons using simulated data illustrate the usefulness of our approach.Item Biological and residual activity of candidate larvicide formulation, SumiLarv 2MR, against an exotic invasive mosquito Anopheles stephensi Liston, 1901 (Diptera: Culicidae) in Ethiopia(Springer Nature, 2025-01-02) Yewhalaw, Delenasaw; Erena, Ebisa; Degefa, Teshome; Kifle, Yehenew Getachew; Zemene, Endalew; Simma, Eba AlemayehuThe study evaluated the efficacy and residual activity of SumiLarv 2MR, SumiLarv 0.5G, and Abate 1SG (used as a positive control) against Anopheles stephensi larvae in Awash Subath Kilo, Afar Regional State, Ethiopia, using a semi-field experimental setup. Plastic containers with capacities of 100L and 250L were used to assess the residual efficacy of SumiLarv 2MR. Specifically, four 100L containers were each treated with one disc of SumiLarv 2MR, compared to two untreated controls. Similarly, four 250L containers received one disc each, with two untreated controls. Additionally, eight 250L containers were treated with a half-dose to match one disc per 500L, alongside four untreated controls. For SumiLarv 0.5G and Abate 1SG, four 100L containers were treated with each larvicide, with two untreated controls for each. Each container received 20� third and fourth instar An. stephensi larvae. Observations of adult emergence were conducted until all pupae either emerged or died. Results showed that SumiLarv 2MR demonstrated a nine-month residual efficacy, SumiLarv 0.5G provided seven weeks of efficacy, and Abate 1SG showed a five-week efficacy. Additionally, SumiLarv 2MR discs retained nearly 50% of their initial pyriproxyfen content after nine months, suggesting potential for extended residual activity. This study highlights the long-term effectiveness of SumiLarv 2MR抯 as a larvicide against An. stephensi in Ethiopia.Item Well-posedness and Sensitivity Analysis of a Fluid Model for Multiclass Many-Server Queues with Abandonment Under Global FCFS DisciplineKang, WeiningIn this paper, under mild conditions on the arrival, service and patience time distributions, we establish the well-posedness of the fluid model of a multiclass many-server queueing model with differentiated service and patience times operated under the global FCFS service discipline. In particular, the well-posedness of the fluid model is established through the study of the existence and uniqueness of fixed points of certain functional map of Volterra type. In addition, by showing a local Lipschitz property of this functional map as a functional of the initial data to the fluid model, we also perform a sensitivity analysis on the fluid model.Item HITTING THE PRIMES FOR THE k-TH TIME TAKES k log(k) DICE ROLLS (ON AVERAGE)ALON, NOGA; Malinovsky, Yaakov; MARTINEZ, LUCY; ZEILBERGER, DORONItem Bayes Estimation of a Common Mean of Several Normal Populations with Unknown Variances(University of Rajshahi, 2024-12-23) Mphekgwana, Peter M.; Kifle, Yehenew Getachew; Marange, Chioneso S.Combining information from several independent normal populations to estimate a common mean parameter has applications in meta-analysis and is an important statistical problem. For this application, Gregurich and Broemeling (1997) and Tu (2012) concentrated on point estimation employing Bayesian techniques to infer about the common mean of two normal populations with unknown variances. In our study, we expand upon their investigation to encompass k normal populations with a common mean, incorporating a range of objective priors. Through the use of two examples, it is discovered that as the hyperparameter ? under a Bayesian framework increases, the performance of the Bayesian technique also improves.IJSS, Vol. 24(2) Special, December, 2024, pp 81-94Item Fluid Model of A Many-Server Queueing Network with Abandonment and Markovian Routing(2024) Kang, Weining; Pang, GuodongThis paper studies a ?uid model for a non-Markovian many-server queueing network with abandonment, where externally arrived and internally routed customers are served under the non-idling global First-Come-First-Serve (FCFS) discipline at each station of many parallel servers. The routing follows a Markovian mechanism. Externally arrived and internally routed customers in each queue may have di?erent service time distributions, as well as di?erent patience time distributions, and all these distributions may depend on the station. The ?uid model dynamics is described by the ?uid contents of externally arrived customers and internally routed customers in each queue (both waiting and receiving service) and a set of four measure-valued processes, tracking the amount of service time each externally arrived customer in service has received, the amount of service time each internally routed customer in service has received, the waiting times of externally arrived customers and the waiting times of internally routed customers in queue. Under mild conditions on the service and patience time distributions, we prove the existence and uniqueness of a solution to the ?uid model equations. We then characterize the invariant states of this ?uid model when the arrival rates are constant. We also establish the convergence of the properly scaled stochastic evolution dynamics to the ?uid model.Item Time-Periodic Solutions for Hyperbolic-Parabolic Systems(2024-12-25) Mosny, Stanislav; Muha, Boris; Schwarzacher, Sebastian; Webster, JustinTime-periodic weak solutions for a coupled hyperbolic-parabolic system are obtained. A linear heat and wave equation are considered on two respective $d$-dimensional spatial domains that share a common $(d-1)$-dimensional interface $\Gamma$. The system is only partially damped, leading to an indeterminate case for existing theory (Galdi et al., 2014). We construct periodic solutions by obtaining novel a priori estimates for the coupled system, reconstructing the total energy via the interface $\Gamma$. As a byproduct, geometric constraints manifest on the wave domain which are reminiscent of classical boundary control conditions for wave stabilizability. We note a ``loss" of regularity between the forcing and solution which is greater than that associated with the heat-wave Cauchy problem. However, we consider a broader class of spatial domains and mitigate this regularity loss by trading time and space differentiations, a feature unique to the periodic setting. This seems to be the first constructive result addressing existence and uniqueness of periodic solutions in the heat-wave context, where no dissipation is present in the wave interior. Our results speak to the open problem of the (non-)emergence of resonance in complex systems, and are readily generalizable to related systems and certain nonlinear cases.Item Confidence Ellipsoids of a Multivariate Normal Mean Vector Based on Noise Perturbed and Synthetic Data with Applications(SSCA, 2024) Basak, Biswajit; Kifle, Yehenew Getachew; Sinha, Bimal K.In this paper we address the problem of constructing a confidence ellipsoid of a multivariate normal mean vector based on a random sample from it. The central issue at hand is the sensitivity of the original data and hence the data cannot be directly used/analyzed. We consider a few perturbations of the original data, namely, noise addition and creation of synthetic data based on the plug-in sampling (PIS) method and the posterior predictive sampling (PPS) method. We review some theoretical results under PIS and PPS which are already available based on both frequentist and Bayesian analysis (Klein and Sinha, 2015, 2016; Guin et al., 2023) and derive the necessary results under noise addition. A theoretical comparison of all the methods based on expected volumes of the confidence ellipsoids is provided. A measure of privacy protection (PP) is discussed and its formulas under PIS, PPS and noise addition are derived and the different methods are compared based on PP. Applications include analysis of two multivariate datasets. The first dataset, with p = 2, is obtained from the latest Annual Social and Economic Supplement (ASEC) conducted by the US Census Bureau in 2023. The second dataset, with p = 3, pertains to renal variables obtained from the book by Harris and Boyd (1995). Using a synthetic version of the original data generated through PIS and PPS methods and also the noise added data, we produce and display the confidence ellipsoids for the unknown mean vector under various scenarios. Finally, the privacy protection measure is evaluated for various methods and different features.Item Improving Gamma Imaging in Proton Therapy by Sanitizing Compton Camera Simulated Patient Data using Neural Networks through the BRIDE Pipeline(UMBC High Performance Computing Facility, 2024) Chen, Michael O.; Hodge, Julian; Jin, Peter L.; Protz, Ella; Wong, Elizabeth; Cham, Mostafa; Gobbert, Matthias; Barajas, Carlos A.Precision medicine in cancer treatment increasingly relies on advanced radiotherapies, such as proton beam radiotherapy, to enhance efficacy of the treatment. When the proton beam in this treatment interacts with patient matter, the excited nuclei may emit prompt gamma ray interactions that can be captured by a Compton camera. The image reconstruction from this captured data faces the issue of mischaracterizing the sequences of incoming scattering events, leading to excessive background noise. To address this problem, several machine learning models such as Feedfoward Neural Networks (FNN) and Recurrent Neural Networks (RNN) were developed in PyTorch to properly characterize the scattering sequences on simulated datasets, including newly-created patient medium data, which were generated by using a pipeline comprised of the GEANT4 and Monte-Carlo Detector Effects (MCDE) softwares. These models were implemented using the novel ‘Big-data REU Integrated Development and Experimentation’ (BRIDE) platform, a modular pipeline that streamlines preprocessing, feature engineering, and model development and evaluation on parallelized GPU processors. Hyperparameter studies were done on the novel patient data as well as on water phantom datasets used during previous research. Patient data was more difficult than water phantom data to classify for both FNN and RNN models. FNN models had higher accuracy on patient medium data but lower accuracy on water phantom data when compared to RNN models. Previous results on several different datasets were reproduced on BRIDE and multiple new models achieved greater performance than in previous research.Item A New Semi-Discretization of the Fully Clamped Euler-Bernoulli Beam Preserving Boundary Observability Uniformly(IEEE, 2024-12-17) Aydin, Ahmet Kaan; Haider, Md Zulfiqur; Özkan Özer, AhmetThis letter extends a Finite Difference model reduction method to the Euler-Bernoulli beam equation with fully clamped boundary conditions. The corresponding partial differential equation (PDE) is exactly observable in the energy space with a single boundary observer in arbitrarily short observation times. However, standard Finite Difference spatial discretization fails to achieve uniform exact observability as the mesh parameter approaches zero, with minimal observation time potentially depending on the filtering parameter. To address this, we propose a Finite Difference algorithm incorporating an averaging operator and discrete multipliers, leveraging Haraux’s theorem on the spectral gap to ensure uniform observability. This approach eliminates the need for artificial viscosity or Fourier filtering. Our method achieves uniform observability for arbitrarily small times with dual observers-the tip moment and average tip velocity-mirroring results from mixed Finite Elements applied to the wave equation with homogeneous Dirichlet boundary conditions, where dual controllers converge to the single controller of the PDE model [Castro, Micu-Numerische Mathematiik’06]. Our reduced model is applicable to more complex systems involving Euler-Bernoulli beam equations.Item Significance of Functional Status Scale in decannulation after pediatric tracheostomy: A single-center, retrospective study(Wolters Kluwer, 2024) Teplitzky, Taylor B.; Randolph, Nicholas Paul; Li, Ji; Pereira, Kevin D.; Gopalakrishnan, Mathangi; Holloway, AdrianBackground: Metrics to successfully predict pediatric decannulation have been ineffective. The Functional Status Scale (FSS) is a validated pediatric scoring system of functional outcomes. The objective of this study was to evaluate if the FSS over time predicts pediatric tracheostomy decannulation. Subjects and Methods: Chart review of patients admitted to the pediatric intensive care unit (PICU) and underwent tracheostomy at a tertiary care children’s hospital from 2010 to 2019. Baseline demographics, comorbidities, tracheostomy indication, decannulation status, and FSS scores were recorded at PICU discharge and 1 and 3 years after tracheostomy. Logistic regression was performed to assess the association of FSS components with decannulation status at 3 years. Results: Fifty-three patients met the inclusion criteria. Forty (75.5%) patients had complete data. There were no decannulations at 1 year. Nine (22.5%) patients were decannulated at 3 years. An abnormal 3-year FSS score in the feeding domain was significantly associated with persistent tracheostomy at 3 years, with an odds ratio of 7.4 (95% confidence interval: 1.5–36.6, P = 0.01). Conclusions: FSS score can predict decannulation in children discharged from the PICU. This information could modify caregiver expectations and guide rehabilitative efforts.Item Strong Stabilization of a 3D Potential Flow via a Weakly Damped von Karman Plate(2021-12-22) Balakrishna, Abhishek; Lasiecka, Irena; Webster, JustinThe elimination of aeroelastic instability (resulting in sustained oscillations of bridges, buildings, airfoils) is a central engineering and design issue. Mathematically, this translates to strong asymptotic stabilization of a 3D flow by a 2D elastic structure. The stabilization (convergence to the stationary set) of a aerodynamic wave-plate model is established here. A 3D potential flow on the half-space has a spatially-bounded von Karman plate embedded in the boundary. The physical model, then, is a Neumann wave equation with low regularity of coupling conditions. Motivated on empirical observations, we examine if intrinsic panel damping can stabilize the subsonic flow-plate system to a stationary point. Several partial results have been established through partial regularization of the model. Without doing so, classical approaches attempting to treat the given wave boundary data have fallen short, owing to the failure of the Lopatinski condition (in the sense of Kreiss, Sakamoto) and the associated regularity defect of the hyperbolic Neumann mapping. Here, we operate on the panel model as in the engineering literature with no regularization or modifications; we completely resolve the question of stability by demonstrating that weak plate damping strongly stabilizes system trajectories. This is accomplished by microlocalizing the wave data (given by the plate) and observing an "anisotropic" a microlocal compensation by the plate dynamics precisely where the regularity of the 3D wave is compromsed (in the characteristic sector). Several additional stability results for both wave and plate subsystems are established to "push" strong stability of the plate onto the flow.Item More on Round-Robin Tournament Models with a Unique Maximum Score(2024-11-04) Malinovsky, YaakovIn this note we extend a recent result showing the uniqueness of the maximum score in a classical round-robin tournament to the round-robin tournament models with equally strong players.Item Entropy stable conservative flux form neural networks(2024-11-04) Liu, Lizuo; Li, Tongtong; Gelb, Anne; Lee, YoonsangWe propose an entropy-stable conservative flux form neural network (CFN) that integrates classical numerical conservation laws into a data-driven framework using the entropy-stable, second-order, and non-oscillatory Kurganov-Tadmor (KT) scheme. The proposed entropy-stable CFN uses slope limiting as a denoising mechanism, ensuring accurate predictions in both noisy and sparse observation environments, as well as in both smooth and discontinuous regions. Numerical experiments demonstrate that the entropy-stable CFN achieves both stability and conservation while maintaining accuracy over extended time domains. Furthermore, it successfully predicts shock propagation speeds in long-term simulations, {\it without} oracle knowledge of later-time profiles in the training data.Item Toward a Task Planning Theory for Robot Hybrid Dynamics(Banff International Research Station for Mathematical Innovation and Discovery, 2020-09-17) Kvalheim, Matthew D.Item MS15D - Matthew Kvalheim: Isochrons from short, noisy data(Dynamics Days Digital 2020, 2020-09-05) Kvalheim, Matthew D.; Wilshin, Simon; Scott, Clayton; Revzen, ShaiItem Matthew Kvalheim: Templates and Anchors: a review of notions of model reduction(DynamicWalking2018, 2018-06-22) Kvalheim, Matthew D.; Revzen, ShaiMatthew Kvalheim: Templates and Anchors: a review of notions of model reduction. Dynamic Walking Conference 2018, Pensacola.Item Geometry and dynamics of circulant systems(AMS, 2020-10-04) Bloch, Anthony; Kvalheim, Matthew D.Item Data driven models of legged locomotion(SPIE, 2015-05-22) Revzen, Shai; Kvalheim, Matthew D.Legged locomotion is a challenging regime both for experimental analysis and for robot design. From biology, we know that legged animals can perform spectacular feats which our machines can only surpass on some specially controlled surfaces such as roads. We present a concise review of the theoretical underpinnings of Data Driven Floquet Analysis (DDFA), an approach for empirical modeling of rhythmic dynamical systems. We provide a review of recent and classical results which justify its use in the analysis of legged systems.