UMBC Mathematics and Statistics Department

Permanent URI for this collectionhttp://hdl.handle.net/11603/56

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Fiducial Inference for Random-Effects Calibration Models: Advancing Reliable Quantification in Environmental Analytical Chemistry
(2025-03-26) Sahu, Soumya; Mathew, Thomas; Gibbons, Robert; Bhaumik, Dulal K.
This article addresses calibration challenges in analytical chemistry by employing a random-effects calibration curve model and its generalizations to capture variability in analyte concentrations. The model is motivated by specific issues in analytical chemistry, where measurement errors remain constant at low concentrations but increase proportionally as concentrations rise. To account for this, the model permits the parameters of the calibration curve, which relate instrument responses to true concentrations, to vary across different laboratories, thereby reflecting real-world variability in measurement processes. Traditional large-sample interval estimation methods are inadequate for small samples, leading to the use of an alternative approach, namely the fiducial approach. The calibration curve that accurately captures the heteroscedastic nature of the data, results in more reliable estimates across diverse laboratory conditions. It turns out that the fiducial approach, when used to construct a confidence interval for an unknown concentration, produces a slightly wider width while achieving the desired coverage probability. Applications considered include the determination of the presence of an analyte and the interval estimation of an unknown true analyte concentration. The proposed method is demonstrated for both simulated and real interlaboratory data, including examples involving copper and cadmium in distilled water.
Fiducial Confidence Intervals for Agreement Measures Among Raters Under a Generalized Linear Mixed Effects Model
(2025-03-06) Sahu, Soumya; Mathew, Thomas; Bhaumik, Dulal K.
A generalization of the classical concordance correlation coefficient (CCC) is considered under a three-level design where multiple raters rate every subject over time, and each rater is rating every subject multiple times at each measuring time point. The ratings can be discrete or continuous. A methodology is developed for the interval estimation of the CCC based on a suitable linearization of the model along with an adaptation of the fiducial inference approach. The resulting confidence intervals have satisfactory coverage probabilities and shorter expected widths compared to the interval based on Fisher Z-transformation, even under moderate sample sizes. Two real applications available in the literature are discussed. The first application is based on a clinical trial to determine if various treatments are more effective than a placebo for treating knee pain associated with osteoarthritis. The CCC was used to assess agreement among the manual measurements of the joint space widths on plain radiographs by two raters, and the computer-generated measurements of digitalized radiographs. The second example is on a corticospinal tractography, and the CCC was once again applied in order to evaluate the agreement between a well-trained technologist and a neuroradiologist regarding the measurements of fiber number in both the right and left corticospinal tracts. Other relevant applications of our general approach are highlighted in many areas including artificial intelligence.
Differential topology of the spaces of asymptotically stable vector fields and Lyapunov functions
(2025-03-21) Kvalheim, Matthew D.
We study the topology of the space of all smooth asymptotically stable vector fields on Rⁿ, as well as the space of all proper smooth Lyapunov functions for such vector fields. We prove that both spaces are path-connected and simply connected when n ≠ 4, 5 and weakly contractible when n ≤ 3. Moreover, both spaces have the weak homotopy type of the nonlinear Grassmannian of submanifolds of Rⁿ diffeomorphic to the n-disc. The proofs rely on Lyapunov theory and differential topology, such as the work of Smale and Perelman on the generalized Poincaré conjecture and results of Smale, Cerf, and Hatcher on the topology of diffeomorphism groups of discs. Applications include a partial answer to a question of Conley, a parametric Hartman-Grobman theorem for nonyperbolic but asymptotically stable equilibria, and a parametric Morse lemma for degenerate minima. We also study the related topics of hyperbolic equilibria, Morse minima, and relative homotopy groups of the space of asymptotically stable vector fields inside the space of those vanishing at a single point.
Sex-specific associations of vitamin D and bone biomarkers with bone density and physical function during recovery from hip fracture: the Baltimore Hip Studies
(Springer Nature, 2025-03-20) Cappola, Anne R.; Abraham, Danielle S.; Kroopnick, Jeffrey M.; Huang, Yi; Hochberg, Marc C.; Miller, Ram R.; Shardell, Michelle; Hicks, Gregory E.; Orwig, Denise; Magaziner, Jay
Less is known about recovery from hip fracture in men. We found differences in 25-hydroxyvitamin D and bone biomarkers between men and women during the year after hip fracture, underscoring the importance of vitamin D assessment in older men and pharmaceutical treatment to reduce bone resorption after hip fracture.
Some commutation principles for optimization problems over transformation groups and semi-FTvN systems
(2025-03-11) Gowda, M. Seetharama; Sossa, David
We introduce the concepts of commutativity relative to a transformation group and strong commutativity in the setting of a semi-FTvN system and show their appearance as optimality conditions in certain optimization problems. In the setting of a semi-FTvN system (in particular, in an FTvN system), we show that strong commutativity implies commutativity and observe that in the special case of Euclidean Jordan algebra, commutativity and strong commutativity concepts reduce, respectively, to those of operator and strong operator commutativity. We demonstrate that every complete hyperbolic polynomial induces a semi-FTvN system. By way of an application, we describe several commutation principles.
Global linearization without hyperbolicity
(2025-02-13) Kvalheim, Matthew D.; Sontag, Eduardo D.
We give a proof of an extension of the Hartman-Grobman theorem to nonhyperbolic but asymptotically stable equilibria of vector fields. Moreover, the linearizing topological conjugacy is (i) defined on the entire basin of attraction if the vector field is complete, and (ii) a C superscript (k ≥ 1) diffeomorphism on the complement of the equilibrium if the vector field is C (superscript k) and the underlying space is not 5-dimensional. We also show that the C (superscript k) statement in the 5-dimensional case is equivalent to the 4-dimensional smooth Poincaré conjecture.
Determination of the residual efficacy of broflanilide (VECTRON™ T500) insecticide for indoor residual spraying in a semi-field setting in Ethiopia
(BMC, 2025-02-13) Simma, Eba Alemayehu; Zegeye, Habtamu; Akessa, Geremew Muleta; Kifle, Yehenew Getachew; Zemene, Endalew; Degefa, Teshome; Yewhalaw, Delenasaw
The rotational use of insecticides with diverse modes of action in indoor residual spraying (IRS) is pivotal for enhancing malaria vector control and addressing insecticide resistance. A key factor in national malaria vector control/elimination programmes is the rate at which these insecticides decay. VECTRON™ T500, with broflanilide as its active ingredient, is a recently developed candidate insecticide formulation which has shown promising results in certain phase II experimental hut trials. However, its residual efficacy across different settings has not been thoroughly investigated. This study evaluated the efficacy of VECTRON™ T500 on various wall surfaces (mud, dung, paint, and cement) and assessed its decay rates over time in Ethiopia.
Uniqueness of Weak Solutions for Biot-Stokes Interactions
(2025-02-10) Avalos, George; Webster, Justin
We resolve the issue of uniqueness of weak solutions for linear, inertial fluid-poroelastic-structure coupled dynamics. The model comprises a 3D Biot poroelastic system coupled to a 3D incompressible Stokes flow via a 2D interface, where kinematic, stress-matching, and tangential-slip conditions are prescribed. Our previous work provided a construction of weak solutions, these satisfying an associated finite energy inequality. However, several well-established issues related to the dynamic coupling, hinder a direct approach to obtaining uniqueness and continuous dependence. In particular, low regularity of the hyperbolic (Lam\'e) component of the model precludes the use of the solution as a test function, which would yield the necessary a priori estimate. In considering degenerate and non-degenerate cases separately, we utilize two different approaches. In the former, energy estimates are obtained for arbitrary weak solutions through a systematic decoupling of the constituent dynamics, and well-posedness of weak solutions is inferred. In the latter case, an abstract semigroup approach is utilized to obtain uniqueness via a precise characterization of the adjoint of the dynamics operator. The results here can be adapted to other systems of poroelasticity, as well as to the general theory of weak solutions for hyperbolic-parabolic coupled systems.
Inference about a Common Mean Vector from Several Independent Multinormal Populations with Unequal and Unknown Dispersion Matrices
(MDPI, 2024-08-31) Kifle, Yehenew Getachew; Moluh, Alain M.; Sinha, Bimal K.
This paper addresses the problem of making inferences about a common mean vector from several independent multivariate normal populations with unknown and unequal dispersion matrices. We propose an unbiased estimator of the common mean vector, along with its asymptotic estimated variance, which can be used to test hypotheses and construct confidence ellipsoids, both of which are valid for large samples. Additionally, we discuss an approximate method based on generalized p-values. The paper also presents exact test procedures and methods for constructing exact confidence sets for the common mean vector, with a comparison of the local power of these exact tests. The performance of the proposed methods is demonstrated through a simulation study and an application to data from the Current Population Survey (CPS) Annual Social and Economic (ASEC) Supplement 2021 conducted by the U.S. Census Bureau for the Bureau of Labor Statistics.
Semiparametric modeling of time-varying activation and connectivity in task-based fMRI data
(Elsevier, 2020-10-01) Park, Jun Young; Polzehl, Joerg; Chatterjee, Snigdhansu; Brechmann, André; Fiecas, Mark
In functional magnetic resonance imaging (fMRI), there is a rise in evidence that time-varying functional connectivity, or dynamic functional connectivity (dFC), which measures changes in the synchronization of brain activity, provides additional information on brain networks not captured by time-invariant (i.e., static) functional connectivity. While there have been many developments for statistical models of dFC in resting-state fMRI, there remains a gap in the literature on how to simultaneously model both dFC and time-varying activation when the study participants are undergoing experimental tasks designed to probe at a cognitive process of interest. A method is proposed to estimate dFC between two regions of interest (ROIs) in task-based fMRI where the activation effects are also allowed to vary over time. The proposed method, called TVAAC (time-varying activation and connectivity), uses penalized splines to model both time-varying activation effects and time-varying functional connectivity and uses the bootstrap for statistical inference. Simulation studies show that TVAAC can estimate both static and time-varying activation and functional connectivity, while ignoring time-varying activation effects would lead to poor estimation of dFC. An empirical illustration is provided by applying TVAAC to analyze two subjects from an event-related fMRI learning experiment.
The influence of decision-making in tree ring-based climate reconstructions
(Springer Nature, 2021-06-07) Büntgen, Ulf; Allen, Kathy; Anchukaitis, Kevin J.; Arseneault, Dominique; Boucher, Étienne; Bräuning, Achim; Chatterjee, Snigdhansu; Cherubini, Paolo; Churakova (Sidorova), Olga V.; Corona, Christophe; Gennaretti, Fabio; Grießinger, Jussi; Guillet, Sebastian; Guiot, Joel; Gunnarson, Björn; Helama, Samuli; Hochreuther, Philipp; Hughes, Malcolm K.; Huybers, Peter; Kirdyanov, Alexander V.; Krusic, Paul J.; Ludescher, Josef; Meier, Wolfgang J.-H.; Myglan, Vladimir S.; Nicolussi, Kurt; Oppenheimer, Clive; Reinig, Frederick; Salzer, Matthew W.; Seftigen, Kristina; Stine, Alexander R.; Stoffel, Markus; St. George, Scott; Tejedor, Ernesto; Trevino, Aleyda; Trouet, Valerie; Wang, Jianglin; Wilson, Rob; Yang, Bao; Xu, Guobao; Esper, Jan
Tree-ring chronologies underpin the majority of annually-resolved reconstructions of Common Era climate. However, they are derived using different datasets and techniques, the ramifications of which have hitherto been little explored. Here, we report the results of a double-blind experiment that yielded 15 Northern Hemisphere summer temperature reconstructions from a common network of regional tree-ring width datasets. Taken together as an ensemble, the Common Era reconstruction mean correlates with instrumental temperatures from 1794–2016 CE at 0.79 (p < 0.001), reveals summer cooling in the years following large volcanic eruptions, and exhibits strong warming since the 1980s. Differing in their mean, variance, amplitude, sensitivity, and persistence, the ensemble members demonstrate the influence of subjectivity in the reconstruction process. We therefore recommend the routine use of ensemble reconstruction approaches to provide a more consensual picture of past climate variability.
Physics-guided probabilistic modeling of extreme precipitation under climate change
(Springer Nature, 2020-06-24) Kodra, Evan; Bhatia, Udit; Chatterjee, Snigdhansu; Chen, Stone; Ganguly, Auroop Ratan
Earth System Models (ESMs) are the state of the art for projecting the effects of climate change. However, longstanding uncertainties in their ability to simulate regional and local precipitation extremes and related processes inhibit decision making. Existing state-of-the art approaches for uncertainty quantification use Bayesian methods to weight ESMs based on a balance of historical skills and future consensus. Here we propose an empirical Bayesian model that extends an existing skill and consensus based weighting framework and examine the hypothesis that nontrivial, physics-guided measures of ESM skill can help produce reliable probabilistic characterization of climate extremes. Specifically, the model leverages knowledge of physical relationships between temperature, atmospheric moisture capacity, and extreme precipitation intensity to iteratively weight and combine ESMs and estimate probability distributions of return levels. Out-of-sample validation suggests that the proposed Bayesian method, which incorporates physics-guidance, has the potential to derive reliable precipitation projections, although caveats remain and the gain is not uniform across all cases.
On weighted multivariate sign functions
(Elsevier, 2022-05-21) Majumdar, Subhabrata; Chatterjee, Snigdhansu
Multivariate sign functions are often used for robust estimation and inference. We propose using data dependent weights in association with such functions. The proposed weighted sign functions retain desirable robustness properties, while significantly improving efficiency in estimation and inference compared to unweighted multivariate sign-based methods. Using weighted signs, we demonstrate methods of robust location estimation and robust principal component analysis. We extend the scope of using robust multivariate methods to include robust sufficient dimension reduction and functional outlier detection. Several numerical studies and real data applications demonstrate the efficacy of the proposed methodology.
High dimensional, robust, unsupervised record linkage
(Statistics Poland, 2020) Bera, Sabyasachi; Chatterjee, Snigdhansu
We develop a technique for record linkage on high dimensional data, where the two datasets may not have any common variable, and there may be no training set available. Our methodology is based on sparse, high dimensional principal components. Since large and high dimensional datasets are often prone to outliers and aberrant observations, we propose a technique for estimating robust, high dimensional principal components. We present theoretical results validating the robust, high dimensional principal component estimation steps, and justifying their use for record linkage. Some numeric results and remarks are also presented.
Probing an auxiliary laser to tune the repetition rate of a soliton microcomb
(Optica, 2025-02-15) Mahmood, Tanvir; Cahill, James P.; Sykes, Patrick; Courtright, Logan; Wu, Lue; Vahala, Kerry J.; Menyuk, Curtis; Zhou, Weimin
We demonstrate that it is possible to linearly tune the repetition rate of a bright soliton comb that is generated using an Si3N4 microring resonator by linearly varying the frequency of an auxiliary heater laser. Hence, the auxiliary laser can be utilized as a linear active feedback element for stabilizing the repetition rate. We investigated the potential of the auxiliary laser as an actuator of the soliton repetition rate by varying the auxiliary laser frequency at different modulation rates. Within the modulation bandwidth of the laser, we find that the variation ratio, defined as the ratio of the change in the repetition rate to the change in the laser frequency, remains unchanged. This variation ratio also quantifies the correlation between the frequency drift of the auxiliary laser and the repetition rate phase noise and makes it possible to examine the impact of frequency drift on the attainable phase noise performance of the soliton microcomb. For our setup, we find that the repetition rate phase noise of the microcomb below a 1-kHz offset from the carrier is dominated by the frequency drift of the auxiliary laser, which emphasizes the importance of deploying an inherently low-phase-noise laser when auxiliary laser heating technique is utilized.
Chemotaxis of Drosophila Border Cells is Modulated by Tissue Geometry Through Dispersion of Chemoattractants
(Elsevier, 2025-02-05) George, Alexander; Akhavan, Naghmeh; Peercy, Bradford; Starz-Gaiano, Michelle
Migratory cells respond to graded concentrations of diffusible chemoattractants in vitro, but how complex tissue geometries in vivo impact chemotaxis is poorly understood. To address this, we studied the Drosophila border cells. Live-imaged border cells varied in their chemotactic migration speeds, which correlated positionally with distinct architectures. We then developed a reduced mathematical model to determine how chemoattractant distribution is affected by tissue architecture. Larger extracellular volumes locally dampened the chemoattractant gradient and, when coupled with an agent-based motion of the cluster, reduced cell speeds. This suggests that chemoattractant levels vary by tissue architectures, informing cell migration behaviors locally, which we tested in vivo. Genetically elevating chemoattractant levels slowed migration in specific architectural regions, while mutants with spacious tissue structure rescued defects from high chemoattractant levels, promoting punctual migration. Our results highlight the interplay between tissue geometry and the local distribution of signaling molecules to orchestrate cell migration.
Data-Driven Approaches to Classifier and Variable Selection in High-Dimensional Classification
(2024-01-01) Andalib, Vahid; Baek, Seungchul; Mathematics and Statistics; Statistics
Classification in high dimensions has gained significant attention over the past two decades since Fisher's linear discriminant analysis (LDA) is not optimal in a smaller sample size n comparing the number of variables p, i.e., p>n, which is mostly due to the singularity of the sample covariance matrix. This dissertation proposes two novel data-driven approaches to address the challenges in high-dimensional classification, both building upon Fisher's LDA. The first approach involves the development of binary classifiers using random partitioning. Rather than modifying how to estimate the sample covariance and sample mean vector in constructing a classifier, we build two types of high-dimensional classifiers using data splitting, i.e., single data splitting (SDS) and multiple data splitting (MDS). We also present a weighted version of the MDS classifier that further improves classification performance. Each of the split data sets has a smaller size of variables compared to the sample size so that LDA is applicable, and classification results can be combined with respect to minimizing the misclassification rate. We provide theoretical justification backing up our methods by comparing misclassification rates with LDA in high dimensions. The second approach proposes a high-dimensional classifier, which is a two-stage procedure serving variable selection and classification tasks. The variable selection scheme is to select covariates that belong to the discriminative set, and this approach is aimed at obtaining a better classifier, rather than choosing significant variables themselves. In the first stage, we identify discriminative variables by adopting a notion of mirror statistic, proposed recently in the literature, and LDA direction vector obtained from a regularized form of the sample covariance matrix and a James-Stein type estimator for the mean vectors. In the second stage, a new classifier is developed using the selected variables, refined with a modified ?-greedy algorithm to enhance the LDA direction vector. Both approaches are extensively validated through simulation studies and real data analysis, including DNA microarray data sets. Our methods demonstrate superior or comparable performance to existing high-dimensional classifiers, offering improved classification accuracy, effective variable selection, and robustness in various scenarios. This dissertation contributes to the field of high-dimensional statistics by providing novel, theoretically grounded, and effective methods for classification in high-dimensional spaces, with potential applications in genomics, machine learning, and other domains facing the challenges of high-dimensional data analysis.
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 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.
Profile least squares estimation in networks with covariates
(2024-12-20) Chandna, Swati; Bagozzi, Benjamin; Chatterjee, Snigdhansu
Many 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.
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 Alemayehu
The 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.

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