
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 simpletoimplement, samplingbased 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 groundtruth
reachable set for any userspecified approximation accuracy. As...

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, lowwavenumber 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 highfrequency data, and use the resulting prediction of the missing data to seed the frequency sweep of FWI. To...

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 leftinvertible A. Recovery is exact, or stable in the noisy case, when the couples (i, j) are chosen as edges of a wellconnected graph. One possible way of obtaining the solution is as a feasible point of a simple semidefinite program. Furthermore,...

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, seismicwhiledrilling experiments use active drillstring 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 “cocktailparty” mixing model where each receiver records a linear combination of source signals assumed to be statistically independent, and where only one source...

Núñez, Leonardo Zepeda; Hewett, Russell; Taus, Matthias F; Demanet, Laurent
In this work we propose a hybridizable discontinuous Galerkin (hdG) discretization of the highfrequency 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 secondorder 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...

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.

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 socalled “coalescence cascade” until the final droplet is small enough to be completely absorbed.

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...

Kazhdan, David; Bezrukavnikov, Roman; Varshavsky, Yaakov
Let G be a connected reductive group over a local nonarchimedean 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 Lpackets. 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.

Kapranov, Mikhail; Bezrukavnikov, Roman

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.

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 centerofmass 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...

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 quasitwobody 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...

CDF Collaboration; GomezCeballos, Guillelmo; Goncharov, Maxim; Paus, Christoph M. E.
Differential cross sections for the production of Z bosons or offshell photons γ∗ in association with jets are measured in protonantiproton collisions at centerofmass 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 jetmultiplicity final states. Measured...

CMS Collaboration; Apyan, Aram; Barbieri, Richard Alexander; Baty, Austin Alan; Bierwagen, Katharina; Brandt, Stephanie Akemi; Busza, Wit; Cali, Ivan Amos; Di Matteo, Leonardo; GomezCeballos, Guillelmo; Goncharov, Maxim; Gulhan, Doga Can; Klute, Markus; Lai, Yue Shi; Lee, YenJie; 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, TaWei; 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 centreofmass 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...

Giles, M. B.; VidalCodina, Ferran; Nguyen, Ngoc Cuong; Peraire, Jaime
We present an empirical interpolation and modelvariance 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 realtime computation of reduced basis (RB) outputs approximating highfidelity outputs computed with the hybridizable discontinuous Galerkin (HDG) discretization; (2) the empirical interpolation for an efficient offlineonline decoupling of the parametric and stochastic inuence; and (3) a multilevel variance reduction method that exploits the statistical correlation between the lowfidelity approximations and the highfidelity HDG dis cretization to accelerate the convergence of the Monte Carlo simulations. The multilevel...

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 wellbehaved 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...

Gaul, L. H.; Griffiths, I. M.; Thomson, Stuart
In longdistance 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...

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.; SeitzMoskaliuk, 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 custommade ultraprecise highvoltage dividers were developed and built in cooperation with the German national metrology institute PhysikalischTechnische 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...

Ivy, Diane J
Based on observations of the chlorofluorocarbons CFC13 (chlorotrifluoromethane), 6CFC114 (combined measurement of both isomers of dichlorotetrafluoroethane), and CFC115 (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 12box atmospheric transport model. For CFC13, we provide the first comprehensive global analysis. This compound increased monotonically from its...