arXiv subjects
Publications and source records attributed to David Lee.
In this article, we classify all distributional solutions of $f(-Δ)u=f(1)u$ where $f$ is a non-constant Bernstein function. Specifically, we show that the Fourier transform of $u$ is a single-layer distribution on the unit sphere. Examples of such operators include $(-Δ)^σ$ (for $σ\in (0,1]$), $\log(1-Δ)$ and $(-Δ)^\frac{1}{2}\text{tanh}((-Δ)^\frac{1}{2})$.
The Medium-Resolution Spectrometer (MRS) provides one of the four operating modes of the Mid-Infrared Instrument (MIRI) on board the James Webb Space Telescope (JWST). The MRS is an integral field spectrometer, measuring the spatial and spectral distributions of light across the 5-28 $μm$ wavelength range with a spectral resolving power between 3700-1300. We present the MRS's optical, spectral, and spectro-photometric performance, as achieved in flight, and we report on the effects that limit the instrument's ultimate sensitivity. The MRS flight performance has been quantified using observations of stars, planetary nebulae, and planets in our Solar System. The precision and accuracy of this calibration was checked against celestial calibrators with well-known flux levels and spectral features. We find that the MRS geometric calibration has a distortion solution accuracy relative to the commanded position of 8 mas at 5 $μm$ and 23 mas at 28 $μm$. The wavelength calibration is accurate to within 9 km/sec at 5 $μm$ and 27 km/sec at 28 $μm$. The uncertainty in the absolute spectro-photometric calibration accuracy was estimated at 5.6 +- 0.7 %. The MIRI calibration pipeline is able to suppress the amplitude of spectral fringes to below 1.5 % for both extended and point sources across the entire wavelength range. The MRS point spread function (PSF) is 60 % broader than the diffraction limit along its long axis at 5 $μm$ and is 15 % broader at 28 $μm$. The MRS flight performance is found to be better than prelaunch expectations. The MRS is one of the most subscribed observing modes of JWST and is yielding many high-profile publications. It is currently humanity's most powerful instrument for measuring the mid-infrared spectra of celestial sources and is expected to continue as such for many years to come.
Humans display the remarkable ability to sense the world through tools and other held objects. For example, we are able to pinpoint impact locations on a held rod and tell apart different textures using a rigid probe. In this work, we consider how we can enable robots to have a similar capacity, i.e., to embody tools and extend perception using standard grasped objects. We propose that vibro-tactile sensing using dynamic tactile sensors on the robot fingers, along with machine learning models, enables robots to decipher contact information that is transmitted as vibrations along rigid objects. This paper reports on extensive experiments using the BioTac micro-vibration sensor and a new event dynamic sensor, the NUSkin, capable of multi-taxel sensing at 4~kHz. We demonstrate that fine localization on a held rod is possible using our approach (with errors less than 1 cm on a 20 cm rod). Next, we show that vibro-tactile perception can lead to reasonable grasp stability prediction during object handover, and accurate food identification using a standard fork. We find that multi-taxel vibro-tactile sensing at sufficiently high sampling rate led to the best performance across the various tasks and objects. Taken together, our results provides both evidence and guidelines for using vibro-tactile perception to extend tactile perception, which we believe will lead to enhanced competency with tools and better physical human-robot-interaction.
In this article, we present a solution to the problem: "Which type of linear operators can be realized by the Dirichlet-to-Neumann operator associated with the operator $-Δ-a(z)\frac{\partial^{2}}{\partial z^2}$ on an extension problem?", which was raised in the pioneering work [Comm. Par.Diff. Equ. 32 (2007)] by Caffarelli and Silvestre. In fact, we even go a step further by replacing the negative Laplace operator $-Δ$ on $\mathbb{R}^{d}$ by an $m$-accretive operator $A$ on a general Banach space $X$ and the Dirichlet-to-Neumann operator by the Dirichlet-to-Wentzell operator. We establish uniqueness of solutions to the extension problem in this general framework, which seems to be new in the literature and independent interest. The aim of this paper is to provide a new Phillips-Bochner type functional calculus which uses probabilistic tools from excursion theory. With our method, we are able to characterize all linear operators $ψ(A)$ among the class $CBF$ of complete Bernstein functions $ψ$, resulting in a new characterization of the famous Phillips' subordination theorem within this class $CBF$.
We present a geometric framework for aligning white matter fiber tracts. By registering fiber tracts between brains, one expects to see overlap of anatomical structures that often provide meaningful comparisons across subjects. However, the geometry of white matter tracts is highly heterogeneous, and finding direct tract-correspondence across multiple individuals remains a challenging problem. We present a novel deformation metric between tracts that allows one to compare tracts while simultaneously obtaining a registration. To accomplish this, fiber tracts are represented by an intrinsic mean along with the deformation fields represented by tangent vectors from the mean. In this setting, one can determine a parallel transport between tracts and then register corresponding tangent vectors. We present the results of bundle alignment on a population of 43 healthy adult subjects.
Reconstruction theorems tackle the problem of building a global distribution on $\mathbb{R}^d$ or on a manifold, given a sufficiently coherent family of local approximations, see [M.Hairer, Invent. Math. 198 (2014), no. 2,269--504], [M,Hairer and Labbé, C, J. Funct. Anal. 273 (2017), no. 8, 2578--2618], [Caravenna, F and Zambotti, L, EMS Surv. Math. Sci. 7 (2020), no. 2, 207--251], [Rinaldi, P and Sclavi, F, J. Math. Anal. Appl. 501 (2021), no. 2, 125215, 14 pp] for examples of such results. In this paper, we establish a reconstruction theorem in the Besov setting, generalising results both of [Caravenna, F and Zambotti, L, EMS Surv. Math. Sci. 7 (2020), no. 2, 207--251] and [M,Hairer and Labbé, C, J. Funct. Anal. 273 (2017), no. 8, 2578--2618]. While [M,Hairer and Labbé, C, J. Funct. Anal. 273 (2017), no. 8, 2578--2618] is written in the context of regularity structures and exploits nontrivial results from wavelet analysis, our calculations follow the more elementary and more general approach of [Caravenna, F and Zambotti, L, EMS Surv. Math. Sci. 7 (2020), no. 2, 207--251]. In particular, as in [Caravenna, F and Zambotti, L, EMS Surv. Math. Sci. 7 (2020), no. 2, 207--251], our results are both stated and proved with tools from the theory of distributions. As an application, we present an alternative proof of a (Besov) Young multiplication theorem which does not require the use of paraproducts.
Despite recent advances in vehicle safety technologies, road traffic accidents still pose a severe threat to human lives and have become a leading cause of premature deaths. In particular, crosswalks present a major threat to pedestrians, but we lack dense behavioral data to investigate the risks they face. Therefore, we propose a comprehensive analytical model for pedestrian potential risk using video footage gathered by road security cameras deployed at such crossings. The proposed system automatically detects vehicles and pedestrians, calculates trajectories by frames, and extracts behavioral features affecting the likelihood of potentially dangerous scenes between these objects. Finally, we design a data cube model by using the large amount of the extracted features accumulated in a data warehouse to perform multidimensional analysis for potential risk scenes with levels of abstraction, but this is beyond the scope of this paper, and will be detailed in a future study. In our experiment, we focused on extracting the various behavioral features from multiple crosswalks, and visualizing and interpreting their behaviors and relationships among them by camera location to show how they may or may not contribute to potential risk. We validated feasibility and applicability by applying it in multiple crosswalks in Osan city, Korea.
A new horizontally explicit/vertically implicit (HEVI) time splitting scheme for atmospheric modelling is introduced, for which the horizontal divergence terms are applied within the implicit vertical substep. The new HEVI scheme is implemented in conjunction with a mixed mimetic spectral element spatial discretisation and semi-implicit vertical time stepping scheme that both preserve the skew-symmetric structure of the non-canonical Hamiltonian form of the equations of motion. Within this context the new HEVI scheme allows for the exact balance of all energetic exchanges in space and time. However since the choice of horizontal fluxes for which this balance is satisfied is not consistent with the horizontal velocity at the end of the time level the scheme still admits a temporal energy conservation error. Linearised eigenvalue analysis shows that similar to a fully implicit method, the new HEVI scheme is neutrally stable for all buoyancy modes, and unlike a second order trapezoidal HEVI scheme is stable for all acoustic modes below a certain horizontal CFL number. The scheme is validated against standard test cases for both planetary and nonhydrostatic regimes. For the planetary scale baroclinic instability test case, the new formulation exhibits a secondary oscillation in the potential to kinetic energy power exchanges, with a temporal frequency approximately four times that exhibited by a horizontally third order, vertically second order trapezoidal scheme. For the nonhydrostatic test case, the vertical upwinding of the potential temperature diagnostic equation is shown to reduce spurious oscillations without altering the energetics of the solution, since this upwinding is performed in an energetically consistent manner. For this test case, which is configured on an affine geometry, the exact balance of energy exchanges allows the model to run stably without any form of dissipation.
Multicrossings, which have previously been defined for classical knots and links, are extended to virtual knots and links. In particular, petal diagrams are shown to exist for all virtual knots.
Clinical case reports are written descriptions of the unique aspects of a particular clinical case, playing an essential role in sharing clinical experiences about atypical disease phenotypes and new therapies. However, to our knowledge, there has been no attempt to develop an end-to-end system to annotate, index, or otherwise curate these reports. In this paper, we propose a novel computational resource platform, CREATe, for extracting, indexing, and querying the contents of clinical case reports. CREATe fosters an environment of sustainable resource support and discovery, enabling researchers to overcome the challenges of information science. An online video of the demonstration can be viewed at https://youtu.be/Q8owBQYTjDc.
Upwinded mass fluxes are described and analysed for advection operators discretised using mixed mimetic spectral elements. This involves a Petrov-Galerkin formulation by which the mass flux test functions are evaluated at downstream locations along velocity characteristics. As for the original mixed mimetic spectral element advection operator, the upwinded mass flux advection operator is conservative, however unlike the original advection operator, which is purely hyperbolic, the upwinded advection operator adds dissipation which is biased towards high wave numbers. The upwinded advection operator also removes the spectral gaps present in the dispersion relation for the original advection operator. As for the original advection operator, a material form advection operator may be constructed by similarly downwinding the trial functions of the tracer gradients. Both methods allow for the recovery of exact energy conservation for an incompressible flow field via skew-symmetric formulations. However these skew-symmetric formulations are once again purely hyperbolic operators which do not suppress oscillations. The scheme is implemented within a shallow water code on the sphere in order to diagnose and interpolate the potential vorticity. In the absence of other dissipation terms, it is shown to yield more coherent results for a standard test case of barotropic instability.
An energetically balanced, implicit integrator for non-hydrostatic vertical atmospheric dynamics on the sphere is presented. The integrator allows for the exact balance of energy exchanges in space and time for vertical atmospheric motions by preserving the skew-symmetry of the non-canonical Hamiltonian formulation of the compressible Euler equations. The performance of the integrator is accelerated by a preconditioning strategy that reduces the dimensionality of the inner linear system. Here we reduce the four component velocity, density, density weighted potential temperature and Exner pressure system into a single equation for the density weighted potential temperature via repeated Schur complement decomposition and the careful selection of coupling terms. As currently formulated, the integrator is based on a horizontal-vertical spatial splitting that does not permit bottom topography. The integrator is validated for standard test cases for baroclinic instability and a non-hydrostatic gravity wave on the sphere and a rising bubble in a high-resolution planar geometry, and shows robust convergence across all of these regimes.
The constructive and destructive interference in different layers of the James Webb Space Telescope (JWST) Mid-Infrared Instrument (MIRI) detector arrays modulate the detected signal as a function of wavelength. Additionally, sources of different spatial profiles show different fringe patterns. Dividing by a static fringe flat could hamper the scientific interpretation of sources whose fringes do not match that of the fringe flat. We find point source fringes measured by the MIRI Medium-Resolution Spectrometer (MRS) to be reproducible under similar observing conditions. We want, thus, to identify the variables, if they exist, that would allow for a parametrization of the signal variations induced by point source fringe modulations. We do this by analyzing MRS detector plane images acquired on the ground. We extracted the fringe profile of multiple point source observations and studied the amplitude and phase of the fringes as a function of field position and pixel sampling of the point spread function of the optical chain. A systematic variation in the amplitude and phase of the point source fringes is found over the wavelength range covered by the test sources (4.9-5.8 $μ$m). The variation depends on the fraction of the point spread function seen by the detector pixel. We identify the non-uniform pixel illumination as the root cause of the reported systematic variation. We report an improvement after correction of 50% on the 1$σ$ standard deviation of the spectral continuum. A 50% improvement is also reported in line sensitivity for a benchmark test with a spectral continuum of 100 mJy. The improvement in the shape of weak lines is illustrated using a T Tauri model spectrum. Consequently, we verify that fringes of extended sources and potentially semi-extended sources and crowded fields can be simulated by combining multiple point source fringe transmissions.
Machine-learning (ML) hardware and software system demand is burgeoning. Driven by ML applications, the number of different ML inference systems has exploded. Over 100 organizations are building ML inference chips, and the systems that incorporate existing models span at least three orders of magnitude in power consumption and five orders of magnitude in performance; they range from embedded devices to data-center solutions. Fueling the hardware are a dozen or more software frameworks and libraries. The myriad combinations of ML hardware and ML software make assessing ML-system performance in an architecture-neutral, representative, and reproducible manner challenging. There is a clear need for industry-wide standard ML benchmarking and evaluation criteria. MLPerf Inference answers that call. In this paper, we present our benchmarking method for evaluating ML inference systems. Driven by more than 30 organizations as well as more than 200 ML engineers and practitioners, MLPerf prescribes a set of rules and best practices to ensure comparability across systems with wildly differing architectures. The first call for submissions garnered more than 600 reproducible inference-performance measurements from 14 organizations, representing over 30 systems that showcase a wide range of capabilities. The submissions attest to the benchmark's flexibility and adaptability.
This paper reviews the NTIRE 2020 Challenge on NonHomogeneous Dehazing of images (restoration of rich details in hazy image). We focus on the proposed solutions and their results evaluated on NH-Haze, a novel dataset consisting of 55 pairs of real haze free and nonhomogeneous hazy images recorded outdoor. NH-Haze is the first realistic nonhomogeneous haze dataset that provides ground truth images. The nonhomogeneous haze has been produced using a professional haze generator that imitates the real conditions of haze scenes. 168 participants registered in the challenge and 27 teams competed in the final testing phase. The proposed solutions gauge the state-of-the-art in image dehazing.
Recently, we demonstrated how an astrophotonic light reformatting device, based on a multicore fibre photonic lantern and a three-dimensional waveguide component, can be used to efficiently reformat the point spread function of a telescope to a diffraction-limited psuedo-slit [arXiv:1512.07309]. Here, we demonstrate how such a device can also efficiently mitigate modal noise -- a potential source of instability in high resolution multi-mode fibre-fed spectrographs). To investigate the modal noise performance of the photonic reformatter, we have used it to feed light into a bench-top near-infrared spectrograph (R {\approx} 9,500, λ {\approx} 1550 nm). One approach to quantifying the modal noise involved the use of broadband excitation light and a statistical analysis of how the overall measured spectrum was affected by variations in the input coupling conditions. This approach indicated that the photonic reformatter could reduce modal noise by a factor of six when compared to a multi-mode fibre with a similar number of guided modes. Another approach to quantifying the modal noise involved the use of multiple spectrally narrow lines, and an analysis of how the measured barycentres of these lines were affected by variations in the input coupling. Using this approach, the photonic reformatter was observed to suppress modal noise to the level necessary to obtain spectra with stability close to that observed when using a single mode fibre feed. These results demonstrate the potential of using photonic reformatters to enable efficient multi-mode spectrographs that operate at the diffraction limit and are free of modal noise, with potential applications including radial velocity measurements of M-dwarfs.
In a previous article [J. Comp. Phys. $\mathbf{357}$ (2018) 282-304], the mixed mimetic spectral element method was used to solve the rotating shallow water equations in an idealized geometry. Here the method is extended to a smoothly varying, non-affine, cubed sphere geometry. The differential operators are encoded topologically via incidence matrices due to the use of spectral element edge functions to construct tensor product solution spaces in $H(\mathrm{rot})$, $H(\mathrm{div})$ and $L_2$. These incidence matrices commute with respect to the metric terms in order to ensure that the mimetic properties are preserved independent of the geometry. This ensures conservation of mass, vorticity and energy for the rotating shallow water equations using inexact quadrature on the cubed sphere. The spectral convergence of errors are similarly preserved on the cubed sphere, with the generalized Piola transformation used to construct the metric terms for the physical field quantities.
This article presents a generic model for pricing financial derivatives subject to counterparty credit risk. Both unilateral and bilateral types of credit risks are considered. Our study shows that credit risk should be modeled as American style options in most cases, which require a backward induction valuation. To correct a common mistake in the literature, we emphasize that the market value of a defaultable derivative is actually a risky value rather than a risk-free value. Credit value adjustment (CVA) is also elaborated. A practical framework is developed for pricing defaultable derivatives and calculating their CVAs at a portfolio level.