Scholarly Works, Mathematics
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- Approximate Deconvolution Reduced Order ModelingXie, X.; Wells, D.; Wang, Z.; Iliescu, Traian (2016-10-12)This paper proposes a large eddy simulation reduced order model(LES-ROM) framework for the numerical simulation of realistic flows. In this LES-ROM framework, the proper orthogonal decomposition(POD) is used to define the ROM basis and a POD differential filter is used to define the large ROM structures. An approximate deconvolution(AD) approach is used to solve the ROM closure problem and develop a new AD-ROM. This AD-ROM is tested in the numerical simulation of the one-dimensional Burgers equation with a small diffusion coefficient(10^{-3})
- Averages of completely multiplicative functions over the Gaussian integersDonoso, Sebastian; Le, Anh; Moreira, Joel; Sun, Wenbo (2024)
- A biologically accurate model of directional hearing in the parasitoid fly Ormia ochraceaMikel-Stites, Max R.; Salcedo, Mary K.; Socha, John J.; Marek, Paul E.; Staples, Anne E. (Cold Spring Harbor Laboratory, 2021-09-17)Although most binaural organisms localize sound sources using neurological structures to amplify the sounds they hear, some animals use mechanically coupled hearing organs instead. One of these animals, the parasitoid fly Ormia ochracea, has astoundingly accurate sound localization abilities and can locate objects in the azimuthal plane with a precision of 2°, equal to that of humans. This is accomplished despite an intertympanal distance of only 0.5 mm, which is less than 1/100th of the wavelength of the sound emitted by the crickets that it parasitizes. In 1995, Miles et al. developed a model of hearing mechanics in O. ochracea, which works well for incoming sound angles of less than ±30°, but suffers from reduced accuracy (up to 60% error) at higher angles. Even with this limitation, it has served as the basis for multiple bio-inspired microphone designs for decades. Here, we present critical improvements to the classic O. ochracea hearing model based on information from 3D reconstructions of O. ochracea’s tympana. The 3D images reveal that the tympanal organ has curved lateral faces in addition to the flat front-facing prosternal membranes represented in the Miles model. To mimic these faces, we incorporated spatially-varying spring and damper coefficients that respond asymmetrically to incident sound waves, making a new quasi-two-dimensional (q2D) model. The q2D model has high accuracy (average errors of less than 10%) for the entire range of incoming sound angles. This improved biomechanical hearing model can inform the development of new technologies and may help to play a key role in developing improved hearing aids. Significance Statement: The ability to identify the location of sound sources is critical to organismal survival and for technologies that minimize unwanted background noise, such as directional microphones for hearing aids. Because of its exceptional auditory system, the parasitoid fly Ormia ochracea has served as an important model for binaural hearing and a source of bioinspiration for building tiny directional microphones with outsized sound localization abilities. Here, we performed 3D imaging of the fly’s tympanal organs and used the morphological information to improve the current model for hearing in O. ochracea. This model greatly expands the range of biological accuracy from ±30° to all incoming sound angles, providing a new avenue for studies of binaural hearing and further inspiration for fly-inspired technologies.
- Chern-Schwartz-MacPherson classes for Schubert cells in flag manifoldsAluffi, P.; Mihalcea, L. C. (2015-11-12)We obtain an algorithm computing the Chern-Schwartz-MacPherson (CSM) classes of Schubert cells in a generalized flag manifold G/B. In analogy to how the ordinary divided difference operators act on Schubert classes, each CSM class of a Schubert class is obtained by applying certain Demazure-Lusztig type operators to the CSM class of a cell of dimension one less. These operators define a representation of the Weyl group on the homology of G/B. By functoriality, we deduce algorithmic expressions for CSM classes of Schubert cells in any flag manifold G/P. We conjecture that the CSM classes of Schubert cells are an effective combination of (homology) Schubert classes, and prove that this is the case in several classes of examples. We also extend our results and conjectures to the torus equivariant setting.
- Combinatorial curve neighborhoods for the affine flag manifold of type A11Mihalcea, L. C.; Norton, T. (2017)
- Electronic Health Record: Comparative analysis of HL7 and open EHR approachesNestor, 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.
- Energy-Conserving Hermite Methods for Maxwell's EquationsAppelö, 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.
- Fiber-optic SeismologyLindsey, Nathaniel J.; Martin, Eileen R. (2021)Distributed Acoustic Sensing (DAS) is an emerging technology that repurposes a fiber-optic cable as a dense array of strain sensors. This technology repeatedly pings a fiber with laser pulses, measuring optical phase changes in Rayleigh backscattered light. DAS is beneficial for studies of fine-scale processes over multi-kilometer distances, long-term time-lapse monitoring, and deployment in logistically challenging areas (e.g. high temperatures, power limitations, land access barriers). These bene fits have motivated a decade of applications in subsurface imaging and microseismicity monitoring for energy production and carbon sequestration. DAS arrays have recorded microearthquakes, regional earthquakes, teleseisms, and infrastructure signals. Analysis of these wavefields is enabling earthquake seismology where traditional sensors were sparse, as well as structural and near-surface seismology. These studies improved understanding of DAS instrument response through comparison with traditional seismometers. More recently DAS has been used to study cryosphere systems, marine geophysics, geodesy and volcanology. Further advancement of geoscience using DAS requires several community efforts related to instrument access, training, outreach and cyberinfrastructure.
- General boundary value problems of a class of fifth order KdV equations on a bounded intervalSriskandasingam, Mayuran; Sun, Shu Ming; Zhang, Bing-yu Y. (2024)
- Increased risks of mosquito-borne disease emergence in temperate regions of South AmericaEstallo, Elizabet L.; Lopez, Maria Soledad; Luduena-Almeida, Francisco; Madelon, Magali I.; Layun, Federico; Robert, Michael A. (Elsevier, 2024-11-14)
- Increasing arbovirus risk in Chile and neighboring countries in the Southern Cone of South AmericaEollo, Elizabet L.; Sippy, Rachel; Robert, Michael A.; Ayala, Salvador; Pizard, Carlos J. Barboza; Perez-Estigarribia, Pastor E.; Stewart-Ibarra, Anna M. (Elsevier, 2023-06-23)
- The isomorphism problem for Grassmannian Schubert varietiesTarigradschi, 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.
- Joint ergodicity for functions of polynomial growthWe provide necessary and sufficient conditions for joint ergodicity results for systems of commuting measure preserving transformations for an iterated Hardy field function of polynomial growth. Our method builds on and improves recent techniques due to Frantzikinakis and Tsinas, who dealt with multiple ergodic averages along Hardy field functions; it also enhances an approach introduced by the authors and Ferré Moragues to study polynomial iterates.
- A Linear Algorithm for Ambient Seismic Noise Double Beamforming Without CrosscorrelationsMartin, Eileen R. (2020-01-02)Geoscientists and engineers are increasingly using denser arrays for continuous seismic monitoring, and often turning to ambient seismic noise interferometry for low-cost near-surface imaging. While ambient noise interferometry greatly reduces acquisition costs, the computational cost of pair-wise comparisons between all sensors can be prohibitively slow or expensive for applications in engineering and environmental geophysics. Double beamforming of noise correlation functions is a powerful technique to extract body waves from ambient noise, but it is typically performed via pair-wise comparisons between all sensors in two dense array patches (scaling as the product of the number of sensors in one patch with the number of sensors in the other patch). By rearranging the operations involved in the double beamforming transform, we propose a new algorithm that scales as the sum of the number of sensors in two array patches. Compared to traditional double beamforming of noise correlation functions, the new method is more scalable, easily parallelized, and does not require raw data to be exchanged between dense array patches.
- Motivic Chern Classes of Schubert Cells, Hecke Algebras, and Applications to Casselman's ProblemAluffi, Paolo; Mihalcea, Leonardo C.; Schuermann, Joerg; Su, Changjian (Société Mathematique de France, 2024-04-02)Motivic Chern classes are elements in the K-theory of an algebraic variety X, depending on an extra parameter y. They are determined by functoriality and a normalization property for smooth X. In this paper we calculate the motivic Chern classes of Schubert cells in the (equivariant) K-theory of flag manifolds G=B. We show that the motivic class of a Schubert cell is determined recursively by the Demazure-Lusztig operators in the Hecke algebra of the Weyl group of G, starting from the class of a point. The resulting classes are conjectured to satisfy a positivity property. We use the recursions to give a new proof that they are equivalent to certain K-theoretic stable envelopes recently defined by Okounkov and collaborators, thus recovering results of Fehér, Rimányi and Weber. The Hecke algebra action on the K-theory of the Langlands dual flag manifold matches the Hecke action on the Iwahori invariants of the principal series representation associated to an unramified character for a group over a nonarchimedean local field. This gives a correspondence identifying the duals of the motivic Chern classes to the standard basis in the Iwahori invariants, and the fixed point basis to Casselman’s basis. We apply this correspondence to prove two conjectures of Bump, Nakasuji and Naruse concerning factorizations and holomorphy properties of the coefficients in the transition matrix between the standard and the Casselman’s basis.
- Nonlinear Parametric Inversion Using Interpolatory Model Reductionde Sturler, Eric; Gugercin, Serkan; Kilmer, Misha E.; Chaturantabut, Saifon; Beattie, Christopher A.; O'Connell, Meghan (Siam Publications, 2015-01-01)Nonlinear parametric inverse problems appear in several prominent applications; one such application is Diffuse Optical Tomography (DOT) in medical image reconstruction. Such inverse problems present huge computational challenges, mostly due to the need for solving a sequence of large-scale discretized, parametrized, partial diferential equations (PDEs) in the forward model. In this paper, we show how interpolatory parametric model reduction can significantly reduce the cost of the inversion process in DOT by drastically reducing the computational cost of solving the forward problems. The key observation is that function evaluations for the underlying optimization problem may be viewed as transfer function evaluations along the imaginary axis; a similar observation holds for Jacobian evaluations as well. This motivates the use of system-theoretic model order reduction methods. We discuss the construction and use of interpolatory parametric reduced models as surrogates for the full forward model. Within the DOT setting, these surrogate models can approximate both the cost functional and the associated Jacobian with very little loss of accuracy while significantly reducing the cost of the overall inversion process. Four numerical examples illustrate the effciency of the proposed approach. Although we focus on DOT in this paper, we believe that our approach is applicable much more generally.
- On fusing active and passive acoustic sensing for simultaneous localization and mappingBradley, Aidan J.; Abaid, Nicole (2024)Studies on the social behaviors of bats show that they have the ability to eavesdrop on the signals emitted by conspecifics in their vicinity. They can fuse this “passive” data with actively collected data from their own signals to get more information about their environment, allowing them to fly and hunt more efficiently and to avoid or cause jamming when competing for prey. Acoustic sensors are capable of similar feats but are generally used in only an active or passive capacity at one time. Is there a benefit to using both active and passive sensing simultaneously in the same array? In this work we define a family of models for active, passive, and fused sensing systems to measure range and bearing data from an environment defined by point-based landmarks. These measurements are used to solve the problem of simultaneous localization and mapping (SLAM) with extended Kalman filter (EKF) and FastSLAM 2.0 approaches. Our results show agreement with previous findings. Specifically, when active sensing is limited to a narrow angular range, fused sensing can perform just as accurately if not better, while also allowing the sensor to perceive more of the surrounding environment.
- Quantum K theory of partial flag manifoldsMihalcea, 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.
- Requirements for the containment of COVID-19 disease outbreaks through periodic testing, isolation, and quarantineSerrao, Shannon R.; Deng, Shengfeng; Priyanka; Mukhamadiarov, Ruslan I.; Childs, Lauren M.; Täuber, Uwe C. (Virginia Tech, 2020-10-25)We employ individual-based Monte Carlo computer simulations of a stochastic SEIR model variant on a two-dimensional Newman{Watts small-world network to investigate the control of epidemic outbreaks through periodic testing and isolation of infectious individuals, and subsequent quarantine of their immediate contacts. Using disease parameters informed by the COVID-19 pandemic, we investigate the effects of various crucial mitigation features on the epidemic spreading: fraction of the infectious population that is identifiable through the tests; testing frequency; time delay between testing and isolation of positively tested individuals; and the further time delay until quarantining their contacts as well as the quarantine duration. We thus determine the required ranges for these intervention parameters to yield effective control of the disease through both considerable delaying the epidemic peak and massively reducing the total number of sustained infections.