Scholarly Works, Mathematics

Permanent URI for this collection

https://hdl.handle.net/10919/24285

Research articles, presentations, and other scholarship

Browse

Now showing 1 - 20 of 367

Parametric level-sets enhanced to improve reconstruction (PaLEnTIR)
Ozsar, Ege; Kilmer, Misha E.; de Sturler, Eric; Saibaba, Arvind; Miller, Eric L. (IOP, 2025-01-08)
We introduce PaLEnTIR, a significantly enhanced parametric level-set (PaLS) method addressing the restoration and reconstruction of piecewise constant objects. Our key contribution involves a unique PaLS formulation utilizing a single level-set function to restore scenes containing multi-contrast piecewise constant objects without requiring knowledge of the number of objects or their contrasts. Unlike standard PaLS methods employing radial basis functions (RBFs), our model integrates anisotropic basis functions (ABFs), thereby expanding its capacity to represent a wider class of shapes. Furthermore, PaLEnTIR streamlines the model by reducing redundancy and indeterminacy in the parameterization, resulting in improved numerical performance. We compare PaLEnTIR’s performance to state-ofthe art alternatives via a diverse collection of experiments encompassing denoising, deconvolution, sparse and limited angle of view X-ray computed tomography (2D and 3D), and nonlinear diffuse optical tomography (DOT) tasks using both real and
Sum of Squares Approximations to Energy Functions
Adjerid, Hamza; Borggaard, Jeffrey T. (IEEE, 2024-01-01)
Energy functions offer natural extensions of controllability and observability Gramians to nonlinear systems, enabling various applications such as computing reachable sets, optimizing actuator and sensor placement, performing balanced truncation, and designing feedback controllers. However, these extensions to nonlinear systems depend on solving Hamilton-Jacobi-Bellman (HJB) partial differential equations, which are infeasible for large-scale systems. Polynomial approximations are a viable alternative for modest-sized systems, but conventional polynomial approximations may yield negative values of the energy away from the origin. To address this issue, we explore polynomial approximations expressed as a sum of squares to ensure non-negative approximations. In this study, we focus on a reduced sum of squares polynomial where the coefficients are found through least-squares collocation-minimizing the HJB residual at sample points within a desired neighborhood of the origin. We validate the accuracy of these approximations through a case study with a closed-form solution and assess their effectiveness for controlling a ring of van der Pol oscillators with a Laplacian-like coupling term and discretized Burgers equation with source terms.
Algebraic hierarchical locally recoverable codes with nested affine subspace recovery
Haymaker, Kathryn; Malmskog, Beth; Matthews, Gretchen L. (Springer, 2024-10-24)
Codes with locality, also known as locally recoverable codes, allow for recovery of erasures using proper subsets of other coordinates. These subsets are typically of small cardinality to promote recovery using limited network traffic and other resources. Hierarchical locally recoverable codes allow for recovery of erasures using sets of other symbols whose sizes increase as needed to allow for recovery of more symbols. In this paper, we describe a hierarchical recovery structure arising from geometry in Reed–Muller codes and codes with availability from fiber products of curves.We demonstrate how the fiber product hierarchical codes can be viewed as punctured subcodes of Reed–Muller codes, uniting the two constructions. This point of view provides natural structures for local recovery with availability at each level in the hierarchy.
Pedagogical moves related to analogy that support a unified understanding of eigentheory concepts in a quantum mechanics class
Serbin, Kaitlyn Stephens; Wawro, Megan (American Physical Society, 2024-10-30)
It is beneficial for quantum mechanics students to have a unified understanding of eigentheory concepts, so they can recognize the shared structure of mathematized phenomena from the different quantum mechanical systems of spin, energy, or position and recognize those as instantiations of the same overarching concept. Quantum mechanics instructors should, therefore, provide opportunities for their class community to develop a shared unified understanding of eigentheory concepts. One such opportunity can arise by engaging students in analogizing eigentheory concepts in one context with those from another context. We investigate the pedagogical moves related to analogies that can be used by a quantum mechanics course instructor to support a class community in developing a shared unified understanding of eigenequations. We analyze classroom data to characterize an instructor's pedagogical moves as he engaged students in analogical reasoning. Some moves include posing tasks conducive to analogizing; preparing, soliciting, and scaffolding students' participation in analogical reasoning; using deictic gestures and inscriptions; juxtaposing symbols representing the analogized concepts; and explicitly highlighting the sameness of the analogized concepts. We exemplify these pedagogical moves with analytical descriptions of illustrative class episodes. We discuss how these pedagogical moves can support the class community's expansion of their common ground by fostering the development of the class's shared unified understanding of eigentheory concepts.
TCDD and CH223191 alter T cell balance but fail to induce anti-inflammatory response in adult lupus mice
Gutierrez, Fernando; Murphy, Quiyana M.; Swartwout, Brianna K.; Read, Kaitlin A.; Edwards, Michael R.; Abdelhamid, Leila; Cabana-Puig, Xavier; Testerman, James C.; Xu, Tian; Lu, Ran; Amin, Pavly; Cecere, Thomas E.; Reilly, Christopher M.; Oestreich, Kenneth J.; Ciupe, Stanca M.; Luo, Xin M. (The American Association of Immunologists, 2024-02-14)
Aryl hydrocarbon receptor (AhR) responds to endogenous and exogenous ligands as a cytosolic receptor, transcription factor, and E3 ubiquitin ligase. Several studies support an anti-inflammatory effect of AhR activation. However, exposure to the AhR agonist 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) during early stages of development results in an autoimmune phenotype and exacerbates lupus. The effects of TCDD on lupus in adults with pre-existing autoimmunity have not been described. We present novel evidence that AhR stimulation by TCDD alters T cell responses but fails to impact lupus-like disease using an adult mouse model. Interestingly, AhR antagonist CH223191 also changed T cell balance in our model. We next developed a conceptual framework for identifying cellular and molecular factors that contribute to physiological outcomes in lupus and created models that describe cytokine dynamics that were fed into a system of differential equations to predict the kinetics of T follicular helper (Tfh) and regulatory T (Treg) cell populations. The model predicted that Tfh cells expanded to larger values following TCDD exposure compared with vehicle and CH223191. Following the initial elevation, both Tfh and Treg cell populations continuously decayed over time. A function based on the ratio of predicted Treg/Tfh cells showed that Treg cells exceed Tfh cells in all groups, with TCDD and CH223191 showing lower Treg/Tfh cell ratios than the vehicle and that the ratio is relatively constant over time. We conclude that AhR ligands did not induce an anti-inflammatory response to attenuate autoimmunity in adult lupus mice. This study challenges the dogma that TCDD supports an immunosuppressive phenotype.
On the Approximation of Precision Matrices for Wide-Swath Altimetry
Yaremchuk, Max; Beattie, Christopher; Panteleev, Gleb (MDPI, 2024-12-05)
New observations of ocean surface topography obtained by wide-swath satellite interferometry require new capabilities to process spatially correlated errors in order to assimilate these data into numerical models. The sea surface height (SSH) variations have to be weighted against other types of assimilated data using information on their precision, as represented by the inverse of the SSH error covariance matrix R. The latter can be well approximated by a block-circulant (BC) structure and, therefore, allows numerically efficient implementation in operational data assimilation (DA) systems. In this note, we extend the technique of approximating R for wide-swath altimeters by including the uncertainties associated with the state of the atmosphere. It is shown that such an extension keeps the BC approximation error within acceptable (±10%) bounds in a wide range of environmental conditions and could be beneficial for improving the accuracy of SSH retrievals from wide-swath altimeter observations.
Practical Fault Injection Attacks on Constant Time CSIDH and Mitigation Techniques
Chiu, Tinghung; LeGrow, Jason; Xiong, Wenjie (ACM, 2024-11-19)
Commutative Supersingular Isogeny Diffie-Hellman (CSIDH) is an isogeny-based key exchange protocol which is believed to be secure even when parties use long-lived secret keys. To secure CSIDH against side-channel attacks, constant-time implementations with additional dummy isogeny computations are employed. In this study, we demonstrate a fault injection attack on the constant-time real-then-dummy CSIDH to recover the full static secret key. We prototype the attack using voltage glitches on the victim STM32 microcontroller. The attack scheme, which is based on existing research which has yet to be practically implemented, involves getting the faulty output by injecting the fault in a binary search fashion. Our attack reveals many practical factors that were not considered in the previous theoretical fault injection attack analysis, e.g., the probability of a failed fault injection. We bring the practice to theory and developed new complexity analysis of the attack. Further, to mitigate the possible binary search attack on real-then-dummy CSIDH, dynamic random vector CSIDH was proposed previously to randomize the order of real and dummy isogeny operations. We explore fault injection attacks on dynamic random vector CSIDH and evaluate the security level of the mitigation. Our analysis and experimental results demonstrate that it is infeasible to attack dynamic random vector CSIDH in a reasonable amount of time when the success rate of fault injection is not consistent over time.
Bridging Large Eddy Simulation and Reduced-Order Modeling of Convection-Dominated Flows through Spatial Filtering: Review and Perspectives
Quaini, Annalisa; San, Omer; Veneziani, Alessandro; Iliescu, Traian (MDPI, 2024-08-04)
Reduced-order models (ROMs) have achieved a lot of success in reducing the computational cost of traditional numerical methods across many disciplines. In fluid dynamics, ROMs have been successful in providing efficient and relatively accurate solutions for the numerical simulation of laminar flows. For convection-dominated (e.g., turbulent) flows, however, standard ROMs generally yield inaccurate results, usually affected by spurious oscillations. Thus, ROMs are usually equipped with numerical stabilization or closure models in order to account for the effect of the discarded modes. The literature on ROM closures and stabilizations is large and growing fast. In this paper, instead of reviewing all the ROM closures and stabilizations, we took a more modest step and focused on one particular type of ROM closure and stabilization that is inspired by large eddy simulation (LES), a classical strategy in computational fluid dynamics (CFD). These ROMs, which we call LES-ROMs, are extremely easy to implement, very efficient, and accurate. Indeed, LES-ROMs are modular and generally require minimal modifications to standard (“legacy”) ROM formulations. Furthermore, the computational overhead of these modifications is minimal. Finally, carefully tuned LES-ROMs can accurately capture the average physical quantities of interest in challenging convection-dominated flows in science and engineering applications. LES-ROMs are constructed by leveraging spatial filtering, which is the same principle used to build classical LES models. This ensures a modeling consistency between LES-ROMs and the approaches that generated the data used to train them. It also “bridges” two distinct research fields (LES and ROMs) that have been disconnected until now. This paper is a review of LES-ROMs, with a particular focus on the LES concepts and models that enable the construction of LES-inspired ROMs and the bridging of LES and reduced-order modeling. This paper starts with a description of a versatile LES strategy called evolve–filter–relax (EFR) that has been successfully used as a full-order method for both incompressible and compressible convection-dominated flows. We present evidence of this success. We then show how the EFR strategy, and spatial filtering in general, can be leveraged to construct LES-ROMs (e.g., EFR-ROM). Several applications of LES-ROMs to the numerical simulation of incompressible and compressible convection-dominated flows are presented. Finally, we draw conclusions and outline several research directions and open questions in LES-ROM development. While we do not claim this review to be comprehensive, we certainly hope it serves as a brief and friendly introduction to this exciting research area, which we believe has a lot of potential in the practical numerical simulation of convection-dominated flows in science, engineering, and medicine.
Faster Groebner bases for Lie derivatives of ODE systems via monomial orderings
Bessonov, Mariya; Ilmer, Ilia; Konstantinova, Tatiana; Ovchinnikov, Alexey; Pogudin, Gleb; Soto, Pedro (ACM, 2024-07-16)
Symbolic computation for systems of differential equations is often computationally expensive. Many practical differential models have a form of polynomial or rational ODE system with specified outputs. A basic symbolic approach to analyze these models is to compute and then symbolically process the polynomial system obtained by sufficiently many Lie derivatives of the output functions with respect to the vector field given by the ODE system. In this paper, we present a method for speeding up Gröbner basis computation for such a class of polynomial systems by using specific monomial ordering, including weights for the variables, coming from the structure of the ODE model.We provide empirical results that showimprovement across different symbolic computing frameworks and apply the method to speed up structural identifiability analysis of ODE models.
Energy-Conserving Hermite Methods for Maxwell's Equations
Appelö, Daniel; Hagstrom, Thomas; Law-Kam-Cio, Yann-Meing (Springer, 2024-01-22)
Energy-conserving Hermite methods for solving Maxwell's equations in dielectric and dispersive media are described and analyzed. In three space dimensions methods of order $2m$ to $2m+2$ require $(m+1)^3$ degrees-of-freedom per node for each field variable and can be explicitly marched in time with steps independent of $m$. We prove stability for time steps limited only by domain-of-dependence requirements along with error estimates in a special seminorm associated with the interpolation process. Numerical experiments are presented which demonstrate that Hermite methods of very high order enable the efficient simulation of electromagnetic wave propagation over thousands of wavelengths.
Block-Circulant Approximation of the Precision Matrix for Assimilating SWOT Altimetry Data
Yaremchuk, Max; Beattie, Christopher A.; Panteleev, Gleb; D’Addezio, Joseph (MDPI, 2024-05-29)
The recently deployed Surface Water and Ocean Topography (SWOT) mission for the first time has observed the ocean surface at a spatial resolution of 1 km, thus giving an opportunity to directly monitor submesoscale sea surface height (SSH) variations that have a typical magnitude of a few centimeters. This progress comes at the expense of the necessity to take into account numerous uncertainties in calibration of the quality-controlled altimeter data. Of particular importance is the proper filtering of spatially correlated errors caused by the uncertainties in geometry and orientation of the on-board interferometer. These “systematic” errors dominate the SWOT error budget and are likely to have a notable signature in the SSH products available to the oceanographic community. In this study, we explore the utility of the block-circulant (BC) approximation of the SWOT precision matrix developed by the Jet Propulsion Laboratory for assessment of a mission’s accuracy, including the possible impact of the systematic errors on the assimilation of the wide-swath altimeter data into numerical models. It is found that BC approximation of the precision matrix has sufficient (90–99%) accuracy for a wide range of significant wave heights of the ocean surface, and, therefore, could potentially serve as an efficient preconditioner for data assimilation problems involving altimetry observations by space-borne interferometers. An extensive set of variational data assimilation (DA) experiments demonstrates that BC approximation provides more accurate SSH retrievals compared to approximations, assuming a spatially uncorrelated observation error field as is currently adopted in operational DA systems.
Incorporating Intracellular Processes in Virus Dynamics Models
Ciupe, Stanca M.; Conway, Jessica M. (MDPI, 2024-04-30)
In-host models have been essential for understanding the dynamics of virus infection inside an infected individual. When used together with biological data, they provide insight into viral life cycle, intracellular and cellular virus–host interactions, and the role, efficacy, and mode of action of therapeutics. In this review, we present the standard model of virus dynamics and highlight situations where added model complexity accounting for intracellular processes is needed. We present several examples from acute and chronic viral infections where such inclusion in explicit and implicit manner has led to improvement in parameter estimates, unification of conclusions, guidance for targeted therapeutics, and crossover among model systems. We also discuss trade-offs between model realism and predictive power and highlight the need of increased data collection at finer scale of resolution to better validate complex models.
An Integrated Methodological Approach for Documenting Individual and Collective Mathematical Progress: Reinventing the Euler Method Algorithmic Tool
Rasmussen, Chris; Wawro, Megan; Zandieh, Michelle (MDPI, 2024-03-21)
In this paper we advance a methodological approach for documenting the mathematical progress of learners as an integrated analysis of individual and collective activity. Our approach is grounded in and expands the emergent perspective by integrating four analytic constructs: individual meanings, individual participation, collective mathematical practices, and collective disciplinary practices. Using video data of one small group of four students in an inquiry-oriented differential equations classroom, we analyze a 10 min segment in which one small group reinvent Euler’s method, an algorithmic tool for approximating solutions to differential equations. A central intellectual contribution of this work is elaborating and coordinating the four methodological constructs with greater integration, cohesiveness, and coherence.
General boundary value problems of a class of fifth order KdV equations on a bounded interval
Sriskandasingam, Mayuran; Sun, Shu Ming; Zhang, Bing-yu Y. (2024)
Electronic Health Record: Comparative analysis of HL7 and open EHR approaches
Nestor, Mamani Macedo; Garcia Hilares, Nilton Alan; Julio, Pariona Quispe; R, Alarcon Matutti (IEEE, 2010-06-01)
This paper presents a comparative analysis of the main proposals to automatize a Patient’s Health Record in any Medical Center: HL7 and OpenEHR. The methodology includes analyzing each approach, defining some criteria of evaluation, doing a comparative chart, and showing the main conclusions.
Resilient s-ACD for Asynchronous Collaborative Solutions of Systems of Linear Equations
Erlandson, Lucas; Atkins, Zachary; Fox, Alyson; Vogl, Christopher; Miedlar, Agnieszka; Ponce, Colin (IEEE, 2023-09-26)
Solving systems of linear equations is a critical component of nearly all scientific computing methods. Traditional algorithms that rely on synchronization become prohibitively expensive in computing paradigms where communication is costly, such as heterogeneous hardware, edge computing, and unreliable environments. In this paper, we introduce an s-step Approximate Conjugate Directions (s-ACD) method and develop resiliency measures that can address a variety of different data error scenarios. This method leverages a Conjugate Gradient (CG) approach locally while using Conjugate Directions (CD) globally to achieve asynchronicity. We demonstrate with numerical experiments that s-ACD admits scaling with respect to the condition number that is comparable with CG on the tested 2D Poisson problem. Furthermore, through the addition of resiliency measures, our method is able to cope with data errors, allowing it to be used effectively in unreliable environments.
Detection of passageways in natural foliage using biomimetic sonar
Wang, Ruihao; Liu, Yimeng; Müller, Rolf (IOP, 2022-08-10)
The ability of certain bat species to navigate in dense vegetation based on trains of short biosonar echoes could provide for an alternative parsimonious approach to obtaining the sensory information that is needed to achieve autonomy in complex natural environments. Although bat biosonar has much lower data rates and spatial (angular) resolution than commonly used human-made sensing systems such as LiDAR or stereo cameras, bat species that live in dense habitats have the ability to reliably detect narrow passageways in foliage. To study the sensory information that the animals may have available to accomplish this, we have used a biomimetic sonar system that was combined with a camera to record echoes and synchronized images from 10 different field sites that featured narrow passageways in foliage. The synchronized camera and sonar data allowed us to create a large data set (130 000 samples) of labeled echoes using a teacher-student approach that used class labels derived from the images to provide training data for echo-based classifiers. The performance achieved in detecting passageways based on the field data closely matched previous results obtained for gaps in an artificial foliage setup in the laboratory. With a deep feature extraction neural network (VGG16) a foliage-versus-passageway classification accuracy of 96.64% was obtained. A transparent artificial intelligence approach (class-activation mapping) indicated that the classifier network relied heavily on the initial rising flank of the echoes. This finding could be exploited with a neuromorphic echo representation that consisted of times where the echo envelope crossed a certain amplitude threshold in a given frequency channel. Whereas a single amplitude threshold was sufficient for this in the previous laboratory study, multiple thresholds were needed to achieve an accuracy of 92.23%. These findings indicate that despite many sources of variability that shape clutter echoes from natural environments, these signals contain sufficient sensory information to enable the detection of passageways in foliage.
Characteristics of departments with high-use of active learning in introductory STEM courses: implications for departmental transformation
Lau, Alexandra C.; Henderson, Charles; Stains, Marilyne; Dancy, Melissa; Merino, Christian; Apkarian, Naneh; Raker, Jeffrey R.; Johnson, Estrella (2024-02-12)
Background: It is well established in the literature that active learning instruction in introductory STEM courses results in many desired student outcomes. Yet, regular use of high-quality active learning is not the norm in many STEM departments. Using results of a national survey, we identified 16 departments where multiple instructors reported using high levels of active learning in their introductory chemistry, mathematics, or physics courses. We conducted interviews with 27 instructors in these 16 departments to better understand the characteristics of such departments. Results: Using grounded theory methodology, we developed a model that highlights relevant characteristics of departments with high use of active learning instruction in their introductory courses. According to this model, there are four main, interconnected characteristics of such departments: motivated people, knowledge about active learning, opportunities, and cultures and structures that support active learning. These departments have one or more people who are motivated to promote the use of active learning. These motivated people have knowledge about active learning as well as access to opportunities to promote the use of active learning. Finally, these departments have cultures and structures that support the use of active learning. In these departments, there is a positive feedback loop that works iteratively over time, where motivated people shape cultures/structures and these cultures/structures in turn increase the number and level of commitment of the motivated people. A second positive feedback loop was found between the positive outcome of using active learning instruction and the strengthening of cultures/structures supportive of active learning. Conclusions: According to the model, there are two main take-away messages for those interested in promoting the use of active learning. The first is that all four components of the model are important. A weak or missing component may limit the desired outcome. The second is that desired outcomes are obtained and strengthened over time through two positive feedback loops. Thus, there is a temporal aspect to change. In all of the departments that were part of our study, the changes took at minimum several years to enact. While our model was developed using only high-use of active learning departments and future work is needed to develop the model into a full change theory, our results do suggest that change efforts may be made more effective by increasing the robustness of the four components and the connections between them.
Quantum K theory of partial flag manifolds
Mihalcea, Constantin; Sharpe, Eric; Gu, Wei; Zhang, Hao; Xu, Weihong; Zou, Hao (Elsevier, 2024-04)
In this paper we use three-dimensional gauged linear sigma models to make physical predictions for Whitney-type presentations of equivariant quantum K theory rings of partial flag manifolds, as quantum products of universal subbundles and various ratios, extending previous work for Grassmannians. Physically, these arise as OPEs of Wilson lines for certain Chern-Simons levels. We also include a simplified method for computing Chern-Simons levels pertinent to standard quantum K theory.
The isomorphism problem for Grassmannian Schubert varieties
Tarigradschi, Mihail; Xu, Weihong (Academic Press – Elsevier, 2023-11-01)
We prove that Schubert varieties in potentially different Grassmannians are isomorphic as varieties if and only if their corresponding Young diagrams are identical up to a transposition. We also discuss a generalization of this result to Grassmannian Richardson varieties. In particular, we prove that Richardson varieties in potentially different Grassmannians are isomorphic as varieties if their corresponding skew diagrams are semi-isomorphic as posets, and we conjecture the converse. Here, two posets are said to be semi-isomorphic if there is a bijection between their sets of connected components such that the corresponding components are either isomorphic or opposite.

Browse

Recent Submissions