UMBC Mathematics and Statistics Department
Permanent URI for this collectionhttp://hdl.handle.net/11603/56
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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.Item Global linearization and fiber bundle structure of invariant manifolds(IOP Science, 2018-08-02) Eldering, Jaap; Kvalheim, Matthew D.; Revzen, ShaiWe study global properties of the global (center-)stable manifold of a normally attracting invariant manifold (NAIM), the special case of a normally hyperbolic invariant manifold (NHIM) with empty unstable bundle. We restrict our attention to continuous-time dynamical systems, or flows. We show that the global stable foliation of a NAIM has the structure of a topological disk bundle, and that similar statements hold for inflowing NAIMs and for general compact NHIMs. Furthermore, the global stable foliation has a Ck disk bundle structure if the local stable foliation is assumed Ck. We then show that the dynamics restricted to the stable manifold of a compact inflowing NAIM are globally topologically conjugate to the linearized transverse dynamics at the NAIM. Moreover, we give conditions ensuring the existence of a global Ck linearizing conjugacy. We also prove a Ck global linearization result for inflowing NAIMs; we believe that even the local version of this result is new, and may be useful in applications to slow-fast systems. We illustrate the theory by giving applications to geometric singular perturbation theory in the case of an attracting critical manifold: we show that the domain of the Fenichel normal form can be extended to the entire global stable manifold, and under additional nonresonance assumptions we derive a smooth global linear normal form.Item Gait modeling and optimization for the perturbed Stokes regime(Springer, 2019-09-01) Kvalheim, Matthew D.; Bittner, Brian; Revzen, ShaiMany forms of locomotion, both natural and artificial, are dominated by viscous friction in the sense that without power expenditure they quickly come to a standstill. From geometric mechanics, it is known that for swimming at the “Stokesian” (viscous; zero Reynolds number) limit, the motion is governed by a reduced-order “connection” model that describes how body shape change produces motion for the body frame with respect to the world. In the “perturbed Stokes regime” where inertial forces are still dominated by viscosity, but are not negligible (low Reynolds number), we show that motion is still governed by a functional relationship between shape velocity and body velocity, but this function is no longer linear in shape change rate. We derive this model using results from singular perturbation theory and the theory of noncompact normally hyperbolic invariant manifolds. Using the theoretical properties of this reduced-order model, we develop an algorithm that estimates an approximation to the dynamics near a cyclic body shape change (a “gait”) directly from observational data of shape and body motion. This extends our previous work which assumed kinematic “connection” models. To compare the old and new algorithms, we analyze simulated swimmers over a range of inertia-to-damping ratios. Our new class of models performs well on the Stokesian regime and over several orders of magnitude outside it into the perturbed Stokes regime, where it gives significantly improved prediction accuracy compared to previous work. In addition to algorithmic improvements, we thereby present a new class of models that is of independent interest. Their application to data-driven modeling improves our ability to study the optimality of animal gaits and our ability to use hardware-in-the-loop optimization to produce gaits for robots.Item Accelerating Subglacial Bed Topography Prediction in Greenland: A Performance Evaluation of Spark-Optimized Machine Learning Models(2024) Cham, Mostafa; Tabassum, Tartela; Shakeri, Ehsan; Wang, JianwuItem Enhancing vision-language models for medical imaging: bridging the 3D gap with innovative slice selection(OpenReview, 2024-11-13) Wang, Yuli; Jian, Peng; Dai, Yuwei; Jones, Craig; Sair, Haris I.; Shen, Jinglai; Loizou, Nicolas; Wu, Jing; Hsu, Wen-Chi; Imami, Maliha Rubaiyat; Jiao, Zhicheng; Zhang, Paul J.; Bai, HarrisonRecent approaches to vision-language tasks are built on the remarkable capabilities of large vision-language models (VLMs). These models excel in zero-shot and few-shot learning, enabling them to learn new tasks without parameter updates. However, their primary challenge lies in their design, which primarily accommodates 2D input, thus limiting their effectiveness for medical images, particularly radiological images like MRI and CT, which are typically 3D. To bridge the gap between state-of-the-art 2D VLMs and 3D medical image data, we developed an innovative, one-pass, unsupervised representative slice selection method called Vote-MI, which selects representative 2D slices from 3D medical imaging. To evaluate the effectiveness of vote-MI when implemented with VLMs, we introduce BrainMD, a robust, multimodal dataset comprising 2,453 annotated 3D MRI brain scans with corresponding textual radiology reports and electronic health records. Based on BrainMD, we further develop two benchmarks, BrainMD-select (including the most representative 2D slice of 3D image) and BrainBench (including various vision-language downstream tasks). Extensive experiments on the BrainMD dataset and its two corresponding benchmarks demonstrate that our representative selection method significantly improves performance in zero-shot and few-shot learning tasks. On average, Vote-MI achieves a 14.6% and 16.6% absolute gain for zero-shot and few-shot learning, respectively, compared to randomly selecting examples. Our studies represent a significant step toward integrating AI in medical imaging to enhance patient care and facilitate medical research. We hope this work will serve as a foundation for data selection as vision-language models are increasingly applied to new tasks.Item Dissipation versus quadratic nonlinearity: from a priori energy bound to higher order regularizing effect(IOP, 2014-02-25) Biswas, Animikh; Tadmor, EitanWe consider a rather general class of convection–diffusion equations, involving dissipation (of possibly fractional order) which competes with quadratic nonlinearities on the regularity of the overall equation. This includes as prototype models, Burgers' equation, the Navier–Stokes equations, the surface quasi-geostrophic equations and the Keller–Segel model for chemotaxis. Here we establish a Petrowsky type parabolic estimate of such equations which entail a precise time decay of higher order Sobolev norms for this class of equations. To this end, we introduce as a main new tool, an ‘infinite-order energy functional’, ε(t):= ∑∞ₙ₌₀ αₙtⁿ∥u(· , t)∥H˙nθ+β꜀ with appropriate Sobolev critical regularity of order β꜀. It captures the regularizing effect of all higher order derivatives of u(·, t), by proving—for a careful, problem-dependent choice of weights {αₙ}, that ε(t) is non-increasing in time.Item Dissipation Length Scale Estimates for Turbulent Flows: A Wiener Algebra Approach(Springer, 2014-06-01) Biswas, Animikh; Jolly, M. S.; Martinez, V. R.; Titi, E. S.In this paper, a lower bound estimate on the uniform radius of spatial analyticity is established for solutions to the incompressible, forced Navier–Stokes system on an n-torus. This estimate matches previously known estimates provided that a certain bound on the initial data is satisfied. In particular, it is argued that for two-dimensional (2D) turbulent flows, the initial data is guaranteed to satisfy this hypothesized bound on a significant portion of the 2D global attractor, in which case, the estimate on the radius matches the best known one found in Kukavica (1998). A key feature in the approach taken here is the choice of the Wiener algebra as the phase space, i.e., the Banach algebra of functions with absolutely convergent Fourier series, whose structure is suitable for the use of the so-called Gevrey norms. We note that the method can also be applied with other phase spaces such as that of the functions with square-summable Fourier series, in which case the estimate on the radius matches that of Doering and Titi (1995). It can then similarly be shown that for three-dimensional (3D) turbulent flows, this estimate holds on a significant portion of the 3D weak attractor.Item Overlapping cusp ion dispersions formed by flux ropes on the day-side magnetopause(frontiers, 2024-08-20) Petrinec, Steven; Connor, Hyunju K.; da Silva, Daniel; Ma, Xuanye; Dorelli, John C.; Porter, Azzan; Girma, Yohannes; Burkholder, BrandonIntroduction: Cusp ion dispersion signatures reflect properties of remote magnetic reconnection. Since the cusp is easier to observe in situ compared to the reconnection x-line, ion dispersions provide key insight on whether reconnection is variable in space and time. This study is motivated by a specific dispersion signature having two ion populations separated in energy but not space. These are known as overlapping dispersions because when observed by low-Earth orbiting satellites traversing the cusp, they appear as two dispersed ion populations overlapping in magnetic latitudes. Overlapping dispersion signatures have been observed for all interplanetary magnetic field (IMF) orientations and have been associated with multiple reconnection processes, but the three-dimensional magnetic reconnection topology and particle trajectories have not been examined.Methods: Forward particle tracing using the GAMERA-CHIMP global magnetohydrodynamic (MHD) with test particle framework is carried out to construct ion dispersion signatures throughout the cusp. Under idealized solar wind driving with steady purely southward IMF, both standard and overlapping dispersions are found.Results: Analysis of the test particle trajectories shows that the higher energy population of the overlapping dispersion travels along the axis of a flux rope before heading into the cusp, whereas the lower energy population goes directly into the cusp. Furthermore, the overlapping dispersions observed by the synthetic satellites compare well to Defense Meteorological Satellite Program (DMSP) F16 observations during strongly southward IMF.Discussion: It is thus concluded that during strongly southward IMF, cusp-entering particles interacting with a magnetopause flux rope (generated by secondary reconnection) is one way to produce an overlapping dispersion. This study lays the groundwork for the forthcoming NASA Tandem Reconnection and Cusp Electrodynamics Reconnaissance Satellites (TRACERS) mission, which will connect the cusp to the magnetosphere—discovering how spatial or temporal variations in magnetic reconnection drive cusp dynamics. The expected launch of TRACERS is in 2025.Item The Use of Guided Reflections in Learning Proof Writing(MDPI, 2024-10-04) Hoffman, Kathleen; Williams, Tory; Kephart, KerrieWe investigated written self-reflections in an undergraduate proof-writing course designed to mitigate the difficulty of a subsequent introductory analysis course. Students wrote weekly self-reflections guided by mechanical, structural, creative, and critical thinking modalities. Our research was guided by three research questions focused on the impact of student self-reflections on student metacognition and performance in the interventional and follow-up class. To address these questions, we categorized the quality of the students’ reflections and calculated their average course grades within each category in the proof-writing, the prerequisite, and the introductory analysis courses. The results demonstrated that writing high-quality self-reflections was a statistically significant predictor of earning higher average course grades in the proof-writing course and the analysis course, but not in the prerequisite course. Convergence over the semester of the students’ self-evaluations toward an experts’ scorings on a modality rubric indicates that students improve in their understanding of the modalities. The repeated writing of guided self-reflections using the framework of the modalities seems to support growth in the students’ awareness of their proof-writing abilities.Item Weighted commutant lifting(ACTA, 1999-04-13) Biswas, Animikh; Foias, Ciprian; Frazho, A. E.This paper presents a refined and constructive version of the commutant lifting theorem (see [14]) which includes the Treil–Volberg generalization of that theorem (see [15]). This theory is used to solve a new variant of the Sarason interpolation problem.Item Extended eigenvalues and the Volterra operator(Cambridge University Press, 2003-02-26) Biswas, Animikh; Lambert, Alan; Petrovic, SrdjanIn this paper we consider the integral Volterra operator on the space L²(0,1). We say that a complex number λ is an extended eigenvalue of V if there exists a nonzero operator X satisfying the equation XV=λVX. We show that the set of extended eigenvalues of V is precisely the interval (0, ∞) and the corresponding eigenvectors may be chosen to be integral operators as well.Item On the general intertwining lifting problem. I(ACTA, 2005-11-08) Biswas, Animikh; Foias, CiprianWe consider the general intertwining lifting problem as formulated in [F1] and which is connected to interpolation problems in reproducing kernel Hilbert spaces. We reduce this general problem to the case where the operators involved are nn block upper-triangular. As a consequence, we show that the causal commutant lifting (see [FT]) and the general intertwining lifting (or extension) problems are equivalent. We also obtain a seemingly new commutant lifting result for the case where one of the operators involved is nilpotent and the other canonical block Jordan. Finally, as an application, we obtain a completely new proof for the Ceausescu--Carswell--Schubert result (see [Ce], [CaS]).Item On the Nile problem by Sir Ronald Fisher(Duke University Press, 2013-07-18) Kagan, Abram M.; Malinovsky, YaakovThe Nile problem by Ronald Fisher may be interpreted as the problem of making statistical inference for a special curved exponential family when the minimal sufficient statistic is incomplete. The problem itself and its versions for general curved exponential families pose a mathematical-statistical challenge: studying the subalgebras of ancillary statistics within the σ-algebra of the (incomplete) minimal sufficient statistics and closely related questions of the structure of UMVUEs. In this paper a new method is developed that, in particular, proves that in the classical Nile problem no statistic subject to mild natural conditions is a UMVUE. The method almost solves an old problem of the existence of UMVUEs. The method is purely statistical (vs. analytical) and works for any family possessing an ancillary statistic. It complements an analytical method that uses only the first order ancillarity (and thus works when the existence of ancillary subalgebras is an open problem) and works for curved exponential families with polynomial constraints on the canonical parameters of which the Nile problem is a special case.Item Monitoring Threshold Functions over Distributed Data Streams with Node Dependent Constraints(MDPI, 2012-09-18) Malinovsky, Yaakov; Kogan, JacobMonitoring data streams in a distributed system has attracted considerable interest in recent years. The task of feature selection (e.g., by monitoring the information gain of various features) requires a very high communication overhead when addressed using straightforward centralized algorithms. While most of the existing algorithms deal with monitoring simple aggregated values such as frequency of occurrence of stream items, motivated by recent contributions based on geometric ideas we present an alternative approach. The proposed approach enables monitoring values of an arbitrary threshold function over distributed data streams through stream dependent constraints applied separately on each stream. We report numerical experiments on a real-world data that detect instances where communication between nodes is required, and compare the approach and the results to those recently reported in the literature.