 Award ID(s):
 1912484
 Publication Date:
 NSFPAR ID:
 10381589
 Journal Name:
 Journal of High Energy Physics
 Volume:
 2022
 Issue:
 3
 ISSN:
 10298479
 Sponsoring Org:
 National Science Foundation
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A bstract Nonlinear sigma models on de Sitter background possess the same kind of derivative interactions as gravity, and show the same sorts of large spacetime logarithms in correlation functions and solutions to the effective field equations. It was recently demonstrated that these logarithms can be resummed by combining a variant of Starobinsky’s stochastic formalism with a variant of the renormalization group. This work considers one of these models and completes two pieces of analysis which were left unfinished: the evolution of the background at two loop order and the one loop beta function.

SUMMARY Accurate synthetic seismic wavefields can now be computed in 3D earth models using the spectral element method (SEM), which helps improve resolution in full waveform global tomography. However, computational costs are still a challenge. These costs can be reduced by implementing a source stacking method, in which multiple earthquake sources are simultaneously triggered in only one teleseismic SEM simulation. One drawback of this approach is the perceived loss of resolution at depth, in particular because highamplitude fundamental mode surface waves dominate the summed waveforms, without the possibility of windowing and weighting as in conventional waveform tomography.
This can be addressed by redefining the costfunction and computing the crosscorrelation wavefield between pairs of stations before each inversion iteration. While the Green’s function between the two stations is not reconstructed as well as in the case of ambient noise tomography, where sources are distributed more uniformly around the globe, this is not a drawback, since the same processing is applied to the 3D synthetics and to the data, and the source parameters are known to a good approximation. By doing so, we can separate time windows with large energy arrivals corresponding to fundamental mode surface waves. This opens the possibility ofmore »
Here we present the results of proof of concept testing of such an approach for a synthetic 3component long period waveform data set (periods longer than 60 s), computed for 273 globally distributed events in a simple toy 3D radially anisotropic upper mantle model which contains shear wave anomalies at different scales. We compare the results of inversion of 10 000 s long stacked timeseries, starting from a 1D model, using source stacked waveforms and stationpair crosscorrelations of these stacked waveforms in the definition of the cost function. We compute the gradient and the Hessian using normal mode perturbation theory, which avoids the problem of crosstalk encountered when forming the gradient using an adjoint approach. We perform inversions with and without realistic noise added and show that the model can be recovered equally well using one or the other cost function.
The proposed approach is computationally very efficient. While application to more realistic synthetic data sets is beyond the scope of this paper, as well as to real data, since that requires additional steps to account for such issues as missing data, we illustrate how this methodology can help inform first order questions such as model resolution in the presence of noise, and tradeoffs between different physical parameters (anisotropy, attenuation, crustal structure, etc.) that would be computationally very costly to address adequately, when using conventional full waveform tomography based on singleevent wavefield computations.

BACKGROUND Optical sensing devices measure the rich physical properties of an incident light beam, such as its power, polarization state, spectrum, and intensity distribution. Most conventional sensors, such as power meters, polarimeters, spectrometers, and cameras, are monofunctional and bulky. For example, classical Fouriertransform infrared spectrometers and polarimeters, which characterize the optical spectrum in the infrared and the polarization state of light, respectively, can occupy a considerable portion of an optical table. Over the past decade, the development of integrated sensing solutions by using miniaturized devices together with advanced machinelearning algorithms has accelerated rapidly, and optical sensing research has evolved into a highly interdisciplinary field that encompasses devices and materials engineering, condensed matter physics, and machine learning. To this end, future optical sensing technologies will benefit from innovations in device architecture, discoveries of new quantum materials, demonstrations of previously uncharacterized optical and optoelectronic phenomena, and rapid advances in the development of tailored machinelearning algorithms. ADVANCES Recently, a number of sensing and imaging demonstrations have emerged that differ substantially from conventional sensing schemes in the way that optical information is detected. A typical example is computational spectroscopy. In this new paradigm, a compact spectrometer first collectively captures the comprehensive spectral information ofmore »

We employ an unregulated computation of the graviton selfenergy from gravitons on the de Sitter background to infer the renormalized result. This is used to quantumcorrect the linearized Einstein equation. We solve this equation for the potentials that represent the gravitational response to a static, point mass. We find large spatial and temporal logarithmic corrections to the Newtonian potential and to the gravitational shift. Although suppressed by a minuscule loopcounting parameter, these corrections cause perturbation theory to break down at large distances and late times. Another interesting fact is that gravitons induce up to three large logarithms, whereas a loop of massless, minimally coupled scalars produces only a single large logarithm. This is in line with corrections to the graviton mode function: a loop of gravitons induces two large logarithms, whereas a scalar loop gives none.

The randompermutation model (RPM) and the idealcipher model (ICM) are idealized models that offer a simple and intuitive way to assess the conjectured standardmodel security of many important symmetrickey and hashfunction constructions. Similarly, the genericgroup model (GGM) captures generic algorithms against assumptions in cyclic groups by modeling encodings of group elements as random injections and allows to derive simple bounds on the advantage of such algorithms. Unfortunately, both wellknown attacks, e.g., based on rainbow tables (Hellman, IEEE Transactions on Information Theory ’80), and more recent ones, e.g., against the discretelogarithm problem (CorriganGibbs and Kogan, EUROCRYPT ’18), suggest that the concrete security bounds one obtains from such idealized proofs are often completely inaccurate if one considers nonuniform or preprocessing attacks in the standard model. To remedy this situation, this work defines the auxiliaryinput (AI) RPM/ICM/GGM, which capture both nonuniform and preprocessing attacks by allowing an attacker to leak an arbitrary (boundedoutput) function of the oracle’s function table; derives the first nonuniform bounds for a number of important practical applications in the AIRPM/ICM, including constructions based on the MerkleDamgård and sponge paradigms, which underly the SHA hashing standards, and for AIRPM/ICM applications with computational security; and using simpler proofs, recovers the AIGGMmore »