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MIT Open Access Articles

Mostrando recursos 181 - 200 de 29.427

  1. Sampling-Based Approximation Algorithms for Reachability Analysis with Provable Guarantees

    Liebenwein, Lucas; Baykal, Cenk; Gilitschenski, Igor; Karaman, Sertac; Rus, Daniela L
    The successful deployment of many autonomous systems in part hinges on providing rigorous guarantees on their performance and safety through a formal verification method, such as reachability analysis. In this work, we present a simple-to-implement, sampling-based algorithm for reachability analysis that is provably optimal up to any desired approximation accuracy. Our method achieves computational efficiency by judiciously sampling a finite subset of the state space and generating an approximate reachable set by conducting reachability analysis on this finite set of states. We prove that the reachable set generated by our algorithm approximates the ground-truth reachable set for any user-specified approximation accuracy. As...

  2. Extrapolated full-waveform inversion (EFWI) with synthesized low-frequency data

    Li, Yunyue; Demanet, Laurent
    The availability of low frequency data is an important factor in the success of full waveform inversion (FWI) in the acoustic regime. The low frequencies help determine the kinematically relevant, low-wavenumber components of the velocity model, which are in turn needed to avoid convergence of FWI to spurious local minima. However, acquiring data below 2 or 3 Hz from the field is a challenging and expensive task. In this paper we explore the possibility of synthesizing the low frequencies computationally from high-frequency data, and use the resulting prediction of the missing data to seed the frequency sweep of FWI. To...

  3. Convex Recovery From Interferometric Measurements

    Demanet, Laurent; Jugnon, Vincent
    This paper discusses some questions that arise when a linear inverse problem involving Ax = b is reformulated in the interferometric framework, where quadratic combinations of b are considered as data in place of b. First, we show a deterministic recovery result for vectors x from measurements of the form (Ax)[subscript i] [bar over (Ax)[subscript j]] for some left-invertible A. Recovery is exact, or stable in the noisy case, when the couples (i, j) are chosen as edges of a well-connected graph. One possible way of obtaining the solution is as a feasible point of a simple semidefinite program. Furthermore,...

  4. Deblending random seismic sources via independent component analysis

    Pisupati, Pawan Bharadwaj; Demanet, Laurent; Fournier, Aime
    We consider the question of deblending for seismic shot records generated from simultaneous random sources at different locations, i.e., how to decompose them into isolated records involving one source at a time. As an example, seismic-while-drilling experiments use active drill-string sources and receivers to look around and ahead of the borehole, but these receivers also record noise from the operation of the drill bit. A conventional method for deblending is independent component analysis (ICA), which assumes a “cocktail-party” mixing model where each receiver records a linear combination of source signals assumed to be statistically independent, and where only one source...

  5. Pollution-free and fast hybridizable discontinuous Galerkin solvers for the high-frequency Helmholtz equation

    Núñez, Leonardo Zepeda; Hewett, Russell; Taus, Matthias F; Demanet, Laurent
    In this work we propose a hybridizable discontinuous Galerkin (hdG) discretization of the high-frequency Helmholtz equation in the presence of point sources and highly heterogeneous and discontinuous wave speed models. We show that it delivers solutions that are provably second-order accurate and do not suffer from the pollution error, as long as a slightly higher order hdG method is used where the polynomial degree is chosen such that p = O(logw). These results hold even if the discontinuities in the wave speed are not resolved by the hdG mesh, as long as the integration procedure used in the assembly of...

  6. Regularity of the Level Set Flow

    Colding, Tobias; Minicozzi, William
    We showed earlier that the level set function of a monotonic advancing front is twice differentiable everywhere with bounded second derivative and satisfies the equation classically. We show here that the second derivative is continuous if and only if the flow has a single singular time where it becomes extinct and the singular set consists of a closed C[superscript 1] manifold with cylindrical singularities. © 2017 Wiley Periodicals, Inc.

  7. Merger of a bubble and a soap film

    Harris, Daniel Martin; Pucci, Giuseppe; Prost, Victor; Quintela Casal, Julio; Bush, John W. M.
    The coalescence of a drop into a fluid bath is a subject of continuing interest in fluid dynamics, owing to its dynamical complexity, its accessibility in the laboratory, and its aesthetic appeal. It has been known for some time that a drop gently placed on a static bath of the same fluid may initially combine only partially with the underlying bath, resulting in a daughter droplet of approximately half the diameter of the parent droplet. This process can then repeat, giving rise to the so-called “coalescence cascade” until the final droplet is small enough to be completely absorbed.

  8. Wreath Macdonald polynomials and the categorical McKay correspondence

    Finkelberg, Michael; Vologodsky, Vadim; Bezrukavnikov, Roman
    Mark Haiman has reduced Macdonald Positivity Conjecture to a statement about geometry of the Hilbert scheme of points on the plane, and formulated a generalization of the conjectures where the symmetric group is replaced by the wreath product Sn[subscript ⋉](Z/rZ)[superscript n]. He has proven the original conjecture by establishing the geometric statement about the Hilbert scheme, as a byproduct he obtained a derived equivalence between coherent sheaves on the Hilbert scheme and coherent sheaves on the orbifold quotient of A[superscript 2n] by the symmetric group Sn. A short proof of a similar derived equivalence for any symplectic quotient singularity has been...

  9. A categorical approach to the stable center conjecture

    Kazhdan, David; Bezrukavnikov, Roman; Varshavsky, Yaakov
    Let G be a connected reductive group over a local non-archimedean field F. The stable center conjecture provides an intrinsic decomposition of the set of equivalence classes of smooth irreducible representations of G(F), which is only slightly coarser than the conjectural decomposition into L-packets. In this work we propose a way to verify this conjecture for depth zero representations. As an illustration of our method, we show that the Bernstein projector to the depth zero spectrum is stable.

  10. Microlocal sheaves and quiver varieties

    Kapranov, Mikhail; Bezrukavnikov, Roman

  11. Reply to Critics

    Rayo, Agustín; Rayo Fierro, Agustin
    Cameron, Eklund, Hofweber, Linnebo, Russell and Sider have written critical essays on my book, The Construction of Logical Space (Oxford: Oxford University Press, 2013). Here I offer some replies.

  12. Measurement of the Branching Fraction ratioB(B[subscript c] ⁺→ψ(2S)π⁺)/B(B[subscript c]⁺→J/ψπ⁺)

    LHCB Collaboration; Ilten, Philip J; Williams, Michael
    Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Using pp collision data collected by LHCb at center-of-mass energies √s = 7 TeV and 8 TeV, corresponding to an integrated luminosity of 3fb⁻¹, the ratio of the branching fraction of the B[subscript c]⁺→ψ(2S)π⁺ decay relative to that of the B[subscript c]⁺→J/ψπ⁺ decay is measured to be 0.268±0.032(stat)±0.007(syst)±0.006(BF). The first uncertainty is statistical, the second is systematic, and the third is due to the uncertainties on the branching fractions of the J/ψ→μ⁺μ⁻ and ψ(2S)→μ⁺μ⁻ decays. This measurement is consistent with...

  13. First Observation and Amplitude Analysis of theB⁻ →D⁺K⁻ π⁻ decay

    LHCB Collaboration; Counts, Ian Thomas Hunt; Ilten, Philip J; Williams, Michael
    The B⁻ →D⁺K⁻ π⁻ decay is observed in a data sample corresponding to 3.0 fb⁻1 of pp collision data recorded by the LHCb experiment during 2011 and 2012. Its branching fraction is measured to be B(B⁻ →D⁺K⁻ π⁻ )=(7.31±0.19±0.22±0.39)×10⁻⁵ where the uncertainties are statistical, systematic and from the branching fraction of the normalization channel B⁻→D⁺π⁻ π⁻ , respectively. An amplitude analysis of the resonant structure of the B⁻ →D⁺K⁻ π⁻ decay is used to measure the contributions from quasi-two-body B⁻ →D*[subscript 0](2400)0K⁻ , B⁻ →D*[subscript 2](2460)⁰K⁻ , and B⁻ →D*[subscript J](2760)0K⁻ decays, as well as from nonresonant sources. The D*[subscript...

  14. Measurement of differential production cross sections for Z/γ* bosons in association with jets in pp¯ collisions at √s = 1.96  TeV

    CDF Collaboration; Gomez-Ceballos, Guillelmo; Goncharov, Maxim; Paus, Christoph M. E.
    Differential cross sections for the production of Z bosons or off-shell photons γ∗ in association with jets are measured in proton-antiproton collisions at center-of-mass energy √s = 1.96  TeV using the full data set collected with the Collider Detector at Fermilab in Tevatron run II and corresponding to 9.6fb⁻¹ of integrated luminosity. Results include first measurements at CDF of differential cross sections in events with a Z/γ∗ boson and three or more jets, the inclusive cross section for production of Z/γ∗ and four or more jets, and cross sections as functions of various angular observables in lower jet-multiplicity final states. Measured...

  15. Measurement of the Z boson differential cross section in transverse momentum and rapidity in proton–proton collisions at 8 TeV

    CMS Collaboration; Apyan, Aram; Barbieri, Richard Alexander; Baty, Austin Alan; Bierwagen, Katharina; Brandt, Stephanie Akemi; Busza, Wit; Cali, Ivan Amos; Di Matteo, Leonardo; Gomez-Ceballos, Guillelmo; Goncharov, Maxim; Gulhan, Doga Can; Klute, Markus; Lai, Yue Shi; Lee, Yen-Jie; Levin, Andrew Michael; Luckey Jr, P David; Niu, Xinmei; Paus, Christoph M. E.; Ralph, Duncan Kelley; Roland, Christof E; Roland, Gunther M; Stephans, George S. F.; Sumorok, Konstanty C; Velicanu, Dragos Alexandru; Veverka, Jan; Wang, Ta-Wei; Wyslouch, Boleslaw; Yang, Ming; Zanetti, Marco; Wyslouch, Victoria
    We present a measurement of the Z boson differential cross section in rapidity and transverse momentum using a data sample of pp collision events at a centre-of-mass energy √s = 8 TeV, corresponding to an integrated luminosity of 19.7 fb ⁻¹. The Z boson is identified via its decay to a pair of muons. The measurement provides a precision test of quantum chromodynamics over a large region of phase space. In addition, due to the small experimental uncertainties in the measurement the data has the potential to constrain the gluon parton distribution function in the kinematic regime important for Higgs...

  16. An Empirical Interpolation and Model-Variance Reduction Method for Computing Statistical Outputs of Parametrized Stochastic Partial Differential Equations

    Giles, M. B.; Vidal-Codina, Ferran; Nguyen, Ngoc Cuong; Peraire, Jaime
    We present an empirical interpolation and model-variance reduction method for the fast and reliable computation of statistical outputs of parametrized stochastic elliptic partial differential equations. Our method consists of three main ingredients: (1) the real-time computation of reduced basis (RB) outputs approximating high-fidelity outputs computed with the hybridizable discontinuous Galerkin (HDG) discretization; (2) the empirical interpolation for an efficient offline-online decoupling of the parametric and stochastic inuence; and (3) a multilevel variance reduction method that exploits the statistical correlation between the low-fidelity approximations and the high-fidelity HDG dis- cretization to accelerate the convergence of the Monte Carlo simulations. The multilevel...

  17. Regular Policies in Abstract Dynamic Programming

    Bertsekas, Dimitri P
    We consider challenging dynamic programming models where the associated Bellman equation, and the value and policy iteration algorithms commonly exhibit complex and even pathological behavior. Our analysis is based on the new notion of regular policies. These are policies that are well-behaved with respect to value and policy iteration, and are patterned after proper policies, which are central in the theory of stochastic shortest path problems. We show that the optimal cost function over regular policies may have favorable value and policy iteration properties, which the optimal cost function over all policies need not have. We accordingly develop a unifying...

  18. Optimizing the breakaway position in cycle races using mathematical modelling

    Gaul, L. H.; Griffiths, I. M.; Thomson, Stuart
    In long-distance competitive cycling, efforts to mitigate the effects of air resistance can significantly reduce the energy expended by the cyclist. A common method to achieve such reductions is for the riders to cycle in one large group, known as the peloton. However, to win a race a cyclist must break away from the peloton, losing the advantage of drag reduction and riding solo to cross the finish line ahead of the other riders. If the rider breaks away too soon then fatigue effects due to the extra pedal force required to overcome the additional drag will result in them...

  19. Calibration of high voltages at the ppm level by the difference of [superscript 83m]Kr conversion electron lines at the KATRIN experiment

    Arenz, M.; Baek, W.-J.; Beck, M.; Beglarian, A.; Behrens, J.; Bergmann, T.; Berlev, A.; Besserer, U.; Blaum, K.; Bode, T.; Bornschein, B.; Bornschein, L.; Brunst, T.; Chilingaryan, S.; Choi, W. Q; Deffert, M.; Doe, P. J; Dragoun, O.; Drexlin, G.; Dyba, S.; Edzards, F.; Eitel, K.; Ellinger, E.; Engel, R.; Enomoto, S.; Erhard, M.; Eversheim, D.; Fedkevych, M.; Fischer, S.; Fränkle, F. M; Franklin, G. B; Friedel, F.; Fulst, A.; Gil, W.; Glück, F.; Ureña, A. G; Grohmann, S.; Grössle, R.; Gumbsheimer, R.; Hackenjos, M.; Hannen, V.; Harms, F.; Haußmann, N.; Heizmann, F.; Helbing, K.; Herz, W.; Hickford, S.; Hilk, D.; Hillesheimer, D.; Howe, M. A; Huber, A.; Jansen, A.; Kellerer, J.; Kernert, N.; Kippenbrock, L.; Kleesiek, M.; Klein, M.; Kopmann, A.; Korzeczek, M.; Kovalík, A.; Krasch, B.; Kraus, M.; Kuckert, L.; Lasserre, T.; Lebeda, O.; Letnev, J.; Lokhov, A.; Machatschek, M.; Marsteller, A.; Martin, E. L; Mertens, S.; Mirz, S.; Monreal, B.; Neumann, H.; Niemes, S.; Off, A.; Osipowicz, A.; Otten, E.; Parno, D. S; Pollithy, A.; Poon, A. W P; Priester, F.; Ranitzsch, P. C; Rest, O.; Robertson, R. G H; Roccati, F.; Rodenbeck, C.; Röllig, M.; Röttele, C.; Ryšavý, M.; Sack, R.; Saenz, A.; Schimpf, L.; Schlösser, K.; Schlösser, M.; Schönung, K.; Schrank, M.; Seitz-Moskaliuk, H.; Sentkerestiová, J.; Slezák, M.; Steidl, M.; Steinbrink, N.; Sturm, M.; Suchopar, M.; Suesser, M.; Telle, H. H; Thorne, L. A; Thümmler, T.; Titov, N.; Tkachev, I.; Trost, N.; Valerius, K.; Vénos, D.; Vianden, R.; Hernández, A. P V; Weber, M.; Weinheimer, C.; Weiss, C.; Welte, S.; Wendel, J.; Wilkerson, J. F; Wolf, J.; Wüstling, S.; Zadoroghny, S.; Buzinsky, Nicholas Gregory; Formaggio, Joseph A; Sibille, Valerian
    The neutrino mass experiment KATRIN requires a stability of 3 ppm for the retarding potential at − 18.6 kV of the main spectrometer. To monitor the stability, two custom-made ultra-precise high-voltage dividers were developed and built in cooperation with the German national metrology institute Physikalisch-Technische Bundesanstalt (PTB). Until now, regular absolute calibration of the voltage dividers required bringing the equipment to the specialised metrology laboratory. Here we present a new method based on measuring the energy difference of two [superscript 83m]Kr conversion electron lines with the KATRIN setup, which was demonstrated during KATRIN’s commissioning measurements in July 2017. The measured scale factor M...

  20. Atmospheric Histories and Emissions of Chlorofluorocarbons CFC-13(CClF[subscript 3]), ΣCFC-114 (C[subscript 2]Cl[subscript 2]F[subscript 4]), and CFC-115 (C[subscript 2]ClF[subscript 5]

    Ivy, Diane J
    Based on observations of the chlorofluorocarbons CFC-13 (chlorotrifluoromethane), 6CFC-114 (combined measurement of both isomers of dichlorotetrafluoroethane), and CFC-115 (chloropentafluoroethane) in atmospheric and firn samples, we reconstruct records of their tropospheric histories spanning nearly 8 decades. These compounds were measured in polar firn air samples, in ambient air archived in canisters, and in situ at the AGAGE (Advanced Global Atmospheric Gases Experiment) network and affiliated sites. Global emissions to the atmosphere are derived from these observations using an inversion based on a 12-box atmospheric transport model. For CFC-13, we provide the first comprehensive global analysis. This compound increased monotonically from its...

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