Multi-trace correlators in the SYK model and non-geometric wormholes

We consider multi-energy level distributions in the SYK model, and in particular, the role of global fluctuations in the density of states of the SYK model. The connected contributions to the moments of the density of states go to zero as N → ∞, however, they are much larger than the standard RMT correlations. We provide a diagrammatic description of the leading behavior of these connected moments, showing that the dominant diagrams are given by 1PI cactus graphs, and derive a vector model of the couplings which reproduces these results. We generalize these results to the first subleading corrections, and to fluctuations of correlation functions. In either case, the new set of correlations between traces (i.e. between boundaries) are not associated with, and are much larger than, the ones given by topological wormholes. The connected contributions that we discuss are the beginning of an infinite series of terms, associated with more and more information about the ensemble of couplings, which hints towards the dual of a single realization. In particular, we suggest that incorporating them in the gravity description requires the introduction of new, lighter and lighter, fields in the bulk with fluctuating boundary couplings.

Machine-Learning of Long-Range Sound Propagation Through Simulated Atmospheric Turbulence

Conventional numerical methods can capture the inherent variability of long-range outdoor sound propagation. However, computational memory and time requirements are high. In contrast, machine-learning models provide very fast predictions. This comes by learning from experimental observations or surrogate data. Yet, it is unknown what type of surrogate data is most suitable for machine-learning. This study used a Crank-Nicholson parabolic equation (CNPE) for generating the surrogate data. The CNPE input data were sampled by the Latin hypercube technique. Two separate datasets comprised 5000 samples of model input. The first dataset consisted of transmission loss (TL) fields for single realizations of turbulence. The second dataset consisted of average TL fields for 64 realizations of turbulence. Three machine-learning algorithms were applied to each dataset, namely, ensemble decision trees, neural networks, and cluster-weighted models. Observational data come from a long-range (out to 8 km) sound propagation experiment. In comparison to the experimental observations, regression predictions have 5–7 dB in median absolute error. Surrogate data quality depends on an accurate characterization of refractive and scattering conditions. Predictions obtained through a single realization of turbulence agree better with the experimental observations.

Optimizing Reservoir Computers for Signal Classification

Reservoir computers are a type of recurrent neural network for which the network connections are not changed. To train the reservoir computer, a set of output signals from the network are fit to a training signal by a linear fit. As a result, training of a reservoir computer is fast, and reservoir computers may be built from analog hardware, resulting in high speed and low power consumption. To get the best performance from a reservoir computer, the hyperparameters of the reservoir computer must be optimized. In signal classification problems, parameter optimization may be computationally difficult; it is necessary to compare many realizations of the test signals to get good statistics on the classification probability. In this work, it is shown in both a spiking reservoir computer and a reservoir computer using continuous variables that the optimum classification performance occurs for the hyperparameters that maximize the entropy of the reservoir computer. Optimizing for entropy only requires a single realization of each signal to be classified, making the process much faster to compute.

Penduga Konsisten dari Fungsi Sebaran dan Fungsi Kepekatan Peluang Waktu Tunggu Proses Poisson Periodik

ABSTRAKPenduga yang konsisten dari fungsi distribusi dan fungsi kepekatan peluang waktu tunggu dari proses Poisson periodik dibahas dalam artikel ini. Tidak ada asumsi bentuk parametrik tertentu dari fungsi intensitas proses Poisson periodik. Situasi dipertimbangkan ketika hanya ada realisasi tunggal dari proses Poisson periodik yang teramati dalam interval terbatas [0,n]. Hasil pembuktian menunjukkan bahwa penduga yang diusulkan konsisten ketika n-??. ABSTRACTThe consistent estimator of the distribution and the density functions of the waiting time of a cyclic Poisson process is considered and investigated. We do not assume any particular parametric form of the intensity function of the cyclic Poisson process. We consider the situation when there is only a single realization of the cyclic Poisson process is spotted in a bounded interval [0,n]. We proved that the propose estimators are consistent as n-??.

Hints of gravitational ergodicity: Berry’s ensemble and the universality of the semi-classical Page curve

Recent developments on black holes have shown that a unitarity-compatible Page curve can be obtained from an ensemble-averaged semi-classical approximation. In this paper, we emphasize (1) that this peculiar manifestation of unitarity is not specific to black holes, and (2) that it can emerge from a single realization of an underlying unitary theory. To make things explicit, we consider a hard sphere gas leaking slowly from a small box into a bigger box. This is a quantum chaotic system in which we expect to see the Page curve in the full unitary description, while semi-classically, eigenstates are expected to behave as though they live in Berry’s ensemble. We reproduce the unitarity-compatible Page curve of this system, semi-classically. The computation has structural parallels to replica wormholes, relies crucially on ensemble averaging at each epoch, and reveals the interplay between the multiple time-scales in the problem. Working with the ensemble averaged state rather than the entanglement entropy, we can also engineer an information “paradox”. Our system provides a concrete example in which the ensemble underlying the semi-classical Page curve is an ergodic proxy for a time average, and not an explicit average over many theories. The questions we address here are logically independent of the existence of horizons, so we expect that semi-classical gravity should also be viewed in a similar light.

LONG-TERM, ENSEMBLE, DATA-ASSIMILATED SHORELINE CHANGE MODELING

We present an ensemble Kalman filter shoreline change model to predict long-term coastal evolution due to waves, sea-level rise, and other natural and anthropogenic processes responsible for sediment transport. The model utilizes ensemble simulations to improve both reliability (via data assimilation) and uncertainty quantification. Coastal change projections exhibit significant differences when simulated with and without ensemble wave conditions. Many long-term coastal change projections rely on a single realization of the future wave climate, often derived from atmospheric conditions simulated by a global climate model. Yet, the single realization approach does not account for the stochastic nature of future wave conditions across a variety of temporal scales (e.g., daily, weekly, seasonally, and interannually). Here, by applying ensemble time series of wave forcing conditions, we demonstrate a sizable increase in model uncertainty compared with the unrealistic case of model projections based on a single realization (e.g., a single time series) of wave forcing.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/V-VwC-cIiQ0

Recovering the Lattice From Its Random Perturbations

Given a $d$-dimensional Euclidean lattice we consider the random set obtained by adding an independent Gaussian vector to each of the lattice points. In this note we provide a simple procedure that recovers the lattice from a single realization of the random set.

Fast robust optimization using bias correction applied to the mean model

Ensemble methods are remarkably powerful for quantifying geological uncertainty. However, the use of the ensemble of reservoir models for robust optimization (RO) can be computationally demanding. The straightforward computation of the expected net present value (NPV) requires many expensive simulations. To reduce the computational burden without sacrificing accuracy, we present a fast and effective approach that requires only simulation of the mean reservoir model with a bias correction factor. Information from distinct controls and model realizations can be used to estimate bias for different controls. The effectiveness of various bias-correction methods and a linear or quadratic approximation is illustrated by two applications: flow optimization in a one-dimensional model and the drilling-order problem in a synthetic field model. The results show that the approximation of the expected NPV from the mean model is significantly improved by estimating the bias correction factor, and that RO with mean model bias correction is superior to both RO performed using a Taylor series representation of uncertainty and deterministic optimization from a single realization. Use of the bias-corrected mean model to account for model uncertainty allows the application of fairly general optimization methods. In this paper, we apply a nonparametric online learning methodology (learned heuristic search) for efficiently computing an optimal or near-optimal robust drilling sequence on the REEK Field example. This methodology can be used either to optimize a complete drilling sequence or to optimize only the first few wells at a reduced cost by limiting the search depths.

A Global Probabilistic Dataset for Monitoring Meteorological Droughts

Accurate and timely drought information is essential to move from postcrisis to preimpact drought-risk management. A number of drought datasets are already available. They cover the last three decades and provide data in near–real time (using different sources), but they are all “deterministic” (i.e., single realization), and input and output data partly differ between them. Here we first evaluate the quality of long-term and continuous climate data for timely meteorological drought monitoring considering the standardized precipitation index. Then, by applying an ensemble approach, mimicking weather/climate prediction studies, we develop Drought Probabilistic (DROP), a new global land gridded dataset, in which an ensemble of observation-based datasets is used to obtain the best near-real-time estimate together with its associated uncertainty. This approach makes the most of the available information and brings it to the end users. The high-quality and probabilistic information provided by DROP is useful for monitoring applications, and may help to develop global policy decisions on adaptation priorities in alleviating drought impacts, especially in countries where meteorological monitoring is still challenging.

Symmetry Analysis of the Stochastic Logistic Equation

We apply the recently developed theory of symmetry of stochastic differential equations to stochastic versions of the logistic equation; these may have environmental or demographical noise, or both—in which case we speak of the complete model. We study all these cases, both with constant and with non-constant noise amplitude, and show that the only one in which there are nontrivial symmetries is that of the stochastic logistic equation with (constant amplitude) environmental noise. In this case, the general theory of symmetry of stochastic differential equations is used to obtain an explicit integration, i.e., an explicit formula for the process in terms of any single realization of the driving Wiener process.