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A global reconfiguration of the magnetotail characterizes substorms. Current sheet thinning, intensification, and magnetic field stretching are defining features of the substorm growth phase and their spatial distributions control the timing and location of substorm onset. Presently, sparse in-situ observations cannot resolve these distributions. A promising approach is to use new substorm magnetic field reconstruction methods based on data mining, termed SST19. Here we compare the SST19 reconstructions to low-altitude ELFIN measurements of energetic particle precipitations to probe the radial profile of the equatorial magnetic field curvature during a 19~August 2022 substorm. ELFIN and SST19 yield a consistent dynamical picture of the magnetotail during the growth phase and capture expected features such as the formation of a thin current sheet and its earthward motion. Furthermore, they resolve a V-like pattern of isotropic electron precipitation boundaries in the time-energy plane, consistent with earlier observations but now over a broad energy range.

When an investor is faced with the option to purchase additional information regarding an asset price, how much should she pay? To address this question, we solve for the indifference price of information in a setting where a trader maximizes her expected utility of terminal wealth over a finite time horizon. If she does not purchase the information, then she solves a partial information stochastic control problem, while, if she does purchase the information, then she pays a cost and receives partial information about the asset's trajectory. We further demonstrate that when the investor can purchase the information at any stopping time prior to the end of the trading horizon, she chooses to do so at a deterministic time.

The heliosphere is permeated with highly structured solar wind originating from the sun. One of the primary science objectives of Parker Solar Probe (PSP) is to determine the structures and dynamics of the plasma and magnetic fields at the sources of the solar wind. However, establishing the connection between in situ measurements and structures and dynamics in the solar atmosphere is challenging: most of the magnetic footpoint mapping techniques have significant uncertainties in the source localization of a plasma parcel observed in situ, and the PSP plasma measurements suffer from a limited field of view. Therefore it lacks a universal tool to self-contextualize the in situ measurements. Here we develop a novel time series visualization method named Jensen-Shannon Scalogram. Utilizing this method, by analyzing the magnetic magnitude data from both PSP and Ulysses, we successfully identify in situ remnants of solar atmospheric and magnetic structures spanning more than seven orders of magnitude, from years to seconds, including polar and mid-latitude coronal holes, as well as structures compatible with super-granulation, ``jetlets'' and very small scale flaring activity. Furthermore, computer simulations of Alfv\'enic turbulence support key features of the observed magnetic magnitude distribution. Building upon these discoveries, the Jensen-Shannon Scalogram therefore not only enables us to reveal the fractal fine structures in the solar wind time series from both PSP and decades-old data archive, but will also serve as a general-purpose data visualization method applicable to all time series.

Resonant interactions between relativistic electrons and electromagnetic ion cyclotron (EMIC) waves provide an effective loss mechanism for this important electron population in the outer radiation belt. The diffusive regime of electron scattering and loss has been well incorporated into radiation belt models within the framework of the quasi-linear diffusion theory, whereas the nonlinear regime has been mostly studied with test particle simulations. There is also a less investigated, nonresonant regime of electron scattering by EMIC waves. All three regimes should be present, depending on the EMIC waves and ambient plasma properties, but the occurrence rates of these regimes have not been previously quantified. This study provides a statistical investigation of the most important EMIC wave-packet characteristics for the diffusive, nonlinear, and nonresonant regimes of electron scattering. We utilize 3 years of Van Allen Probe observations to derive distributions of wave amplitudes, wave-packet sizes, and rates of frequency variations within individual wave-packets. We demonstrate that EMIC waves typically propagate as wave-packets with $\sim 10$ wave periods each, and that $\sim 3-10$\% of such wave-packets can reach the regime of nonlinear resonant interaction with 2 to 6 MeV electrons. We show that EMIC frequency variations within wave-packets reach $50-100$\% of the center frequency, corresponding to a significant high-frequency tail in their wave power spectrum. We explore the consequences of these wave-packet characteristics for high and low energy electron precipitation by H-band EMIC waves and for the relative importance of quasi-linear and nonlinear regimes of wave-particle interactions.

Electron resonant scattering by high-frequency electromagnetic whistler-mode waves has been proposed as a mechanism for solar wind electron scattering and pre-acceleration to energies that enable them to participate in shock drift acceleration around the Earth's bow shock. However, observed whistler-mode waves are often sufficiently intense to resonate with electrons nonlinearly, which prohibits the application of quasi-linear diffusion theory. This is the second of two accompanying papers devoted to developing a new theoretical approach for quantifying the electron distribution evolution subject to multiple resonant interactions with intense whistler-mode wave-packets. In the first paper, we described a probabilistic approach, applicable to systems with short wave-packets. For such systems, nonlinear resonant effects can be treated by diffusion theory, but with diffusion rates different from those of quasi-linear diffusion. In this paper we generalize this approach by merging it with a mapping technique. This technique can be used to model the electron distribution evolution in the presence of significantly non-diffusive resonant scattering by intense long wave-packets. We verify our technique by comparing its predictions with results from a numerical integration approach.

Adiabatic heating of solar wind electrons at the Earth's bow shock and its foreshock region produces transversely anisotropic hot electrons that, in turn, generate intense high-frequency whistler-mode waves. These waves are often detected by spacecraft as narrow-band, electromagnetic emissions in the frequency range of [0.1,0.5] of the local electron gyrofrequency. Resonant interactions between these waves and electrons may cause electron acceleration and pitch-angle scattering, which can be important for creating the electron population that seeds shock drift acceleration. The high intensity and coherence of the observed whistler-mode waves prohibit the use of quasi-linear theory to describe their interaction with electrons. In this paper, we aim to develop a new theoretical approach to describe this interaction, that incorporates nonlinear resonant interactions, gradients of the background density and magnetic field, and the fine structure of the waveforms that usually consist of short, intense wave-packet trains. This is the first of two accompanying papers. It outlines a probabilistic approach to describe the wave-particle interaction. We demonstrate how the wave-packet size affects electron nonlinear resonance at the bow shock and foreshock regions, and how to evaluate electron distribution dynamics in such a system that is frequented by short, intense whistler-mode wave-packets. In the second paper, this probabilistic approach is merged with a mapping technique, which allows us to model systems containing short and long wave-packets.

Electromagnetic ion cyclotron (EMIC) waves lead to rapid scattering of relativistic electrons in Earth's radiation belts, due to their large amplitudes relative to other waves that interact with electrons of this energy range. A central feature of electron precipitation driven by EMIC waves is deeply elusive. That is, moderate precipitating fluxes at energies below the minimum resonance energy of EMIC waves occur concurrently with strong precipitating fluxes at resonance energies in low-altitude spacecraft observations. This paper expands on a previously reported solution to this problem: nonresonant scattering due to wave packets. The quasi-linear diffusion model is generalized to incorporate nonresonant scattering by a generic wave shape. The diffusion rate decays exponentially away from the resonance, where shorter packets lower decay rates and thus widen the energy range of significant scattering. Using realistic EMIC wave packets from $\delta f$ particle-in-cell simulations, test particle simulations are performed to demonstrate that intense, short packets extend the energy of significant scattering well below the minimum resonance energy, consistent with our theoretical prediction. Finally, the calculated precipitating-to-trapped flux ratio of relativistic electrons is compared to ELFIN observations, and the wave power spectra is inferred based on the measured flux ratio. We demonstrate that even with a narrow wave spectrum, short EMIC wave packets can provide moderately intense precipitating fluxes well below the minimum resonance energy., Comment: 32 pages, 9 figures

The trace magnetic power spectrum in the solar wind is known to be characterized by a double power law at scales much larger than the proton gyro-radius, with flatter spectral exponents close to -1 found at the lower frequencies below an inertial range with indices closer to $[-1.5,-1.6]$. The origin of the $1/f$ range is still under debate. In this study, we selected 109 magnetically incompressible solar wind intervals ($\delta |\boldsymbol B|/|\boldsymbol B| \ll 1$) from Parker Solar Probe encounters 1 to 13 which display such double power laws, with the aim of understanding the statistics and radial evolution of the low frequency power spectral exponents from Alfv\'en point up to 0.3 AU. New observations from closer to the sun show that in the low frequency range solar wind turbulence can display spectra much shallower than $1/f$, evolving asymptotically to $1/f$ as advection time increases, indicating a dynamic origin for the $1/f$ range formation. We discuss the implications of this result on the Matteini et al. (2018) conjecture for the $1/f$ origin as well as example spectra displaying a triple power law consistent with the model proposed by Chandran et al. (2018), supporting the dynamic role of parametric decay in the young solar wind. Our results provide new constraints on the origin of the $1/f$ spectrum and further show the possibility of the coexistence of multiple formation mechanisms., Comment: Accepted by ApJL

Thermalization and heating of plasma flows at shocks result in unstable charged-particle distributions which generate a wide range of electromagnetic waves. These waves, in turn, can further accelerate and scatter energetic particles. Thus, the properties of the waves and their implication for wave-particle interactions are critically important for modeling energetic particle dynamics in shock environments. Whistler-mode waves, excited by the electron heat flux or a temperature anisotropy, arise naturally near shocks and foreshock transients. As a result, they can often interact with supra-thermal electrons. The low background magnetic field typical at the core of such transients and the large wave amplitudes may cause such interactions to enter the nonlinear regime. In this study, we present a statistical characterization of whistler-mode waves at foreshock transients around Earth bow shock, as they are observed under a wide range of upstream conditions. We find that a significant portion of them are sufficiently intense and coherent to warrant nonlinear treatment. Copious observations of background magnetic field gradients and intense whistler wave amplitudes suggest that phase trapping, a very effective mechanism for electron acceleration in inhomogeneous plasmas, may be the cause. We discuss the implications of our findings for electron acceleration in planetary and astrophysical shock environments., Comment: Submitted to APJ

This work studies the deep learning-based numerical algorithms for optimal hedging problems in markets with general convex transaction costs on the trading rates, focusing on their scalability of trading time horizon. Based on the comparison results of the FBSDE solver by Han, Jentzen, and E (2018) and the Deep Hedging algorithm by Buehler, Gonon, Teichmann, and Wood (2019), we propose a Stable Transfer Hedging (ST-Hedging) algorithm, to aggregate the convenience of the leading-order approximation formulas and the accuracy of the deep learning-based algorithms. Our ST-Hedging algorithm achieves the same state-of-the-art performance in short and moderately long time horizon as FBSDE solver and Deep Hedging, and generalize well to long time horizon when previous algorithms become suboptimal. With the transfer learning technique, ST-Hedging drastically reduce the training time, and shows great scalability to high-dimensional settings. This opens up new possibilities in model-based deep learning algorithms in economics, finance, and operational research, which takes advantages of the domain expert knowledge and the accuracy of the learning-based methods.

We study a risk-sharing economy where an arbitrary number of heterogenous agents trades an arbitrary number of risky assets subject to quadratic transaction costs. For linear state dynamics, the forward-backward stochastic differential equations characterizing equilibrium asset prices and trading strategies in this context reduce to a system of matrix-valued Riccati equations. We prove the existence of a unique global solution and provide explicit asymptotic expansions that allow us to approximate the corresponding equilibrium for small transaction costs. These tractable approximation formulas make it feasible to calibrate the model to time series of prices and trading volume, and to study the cross-section of liquidity premia earned by assets with higher and lower trading costs. This is illustrated by an empirical case study., Comment: 35 pages, 1 figure

We show how to solve a number of problems in numerical linear algebra, such as least squares regression, $\ell_p$-regression for any $p \geq 1$, low rank approximation, and kernel regression, in time $T(A) \poly(\log(nd))$, where for a given input matrix $A \in \mathbb{R}^{n \times d}$, $T(A)$ is the time needed to compute $A\cdot y$ for an arbitrary vector $y \in \mathbb{R}^d$. Since $T(A) \leq O(\nnz(A))$, where $\nnz(A)$ denotes the number of non-zero entries of $A$, the time is no worse, up to polylogarithmic factors, as all of the recent advances for such problems that run in input-sparsity time. However, for many applications, $T(A)$ can be much smaller than $\nnz(A)$, yielding significantly sublinear time algorithms. For example, in the overconstrained $(1+\epsilon)$-approximate polynomial interpolation problem, $A$ is a Vandermonde matrix and $T(A) = O(n \log n)$; in this case our running time is $n \cdot \poly(\log n) + \poly(d/\epsilon)$ and we recover the results of \cite{avron2013sketching} as a special case. For overconstrained autoregression, which is a common problem arising in dynamical systems, $T(A) = O(n \log n)$, and we immediately obtain $n \cdot \poly(\log n) + \poly(d/\epsilon)$ time. For kernel autoregression, we significantly improve the running time of prior algorithms for general kernels. For the important case of autoregression with the polynomial kernel and arbitrary target vector $b\in\mathbb{R}^n$, we obtain even faster algorithms. Our algorithms show that, perhaps surprisingly, most of these optimization problems do not require much more time than that of a polylogarithmic number of matrix-vector multiplications.

We study risk-sharing equilibria with general convex costs on the agents' trading rates. For an infinite-horizon model with linear state dynamics and exogenous volatilities, we prove that the equilibrium returns mean-revert around their frictionless counterparts - the deviation has Ornstein-Uhlenbeck dynamics for quadratic costs whereas it follows a doubly-reflected Brownian motion if costs are proportional. More general models with arbitrary state dynamics and endogenous volatilities lead to multidimensional systems of nonlinear, fully-coupled forward-backward SDEs. These fall outside the scope of known wellposedness results, but can be solved numerically using the simulation-based deep-learning approach of Han, Jentzen and E (2018). In a calibration to time series of prices and trading volume, realistic liquidity premia are accompanied by a moderate increase in volatility. The effects of different cost specifications are rather similar, justifying the use of quadratic costs as a proxy for other less tractable specifications., Comment: 45 pages, 6 figures

We consider peer review in a conference setting where there is typically an overlap between the set of reviewers and the set of authors. This overlap can incentivize strategic reviews to influence the final ranking of one's own papers. In this work, we address this problem through the lens of social choice, and present a theoretical framework for strategyproof and efficient peer review. We first present and analyze an algorithm for reviewer-assignment and aggregation that guarantees strategyproofness and a natural efficiency property called unanimity, when the authorship graph satisfies a simple property. Our algorithm is based on the so-called partitioning method, and can be thought as a generalization of this method to conference peer review settings. We then empirically show that the requisite property on the authorship graph is indeed satisfied in the submission data from the ICLR conference, and further demonstrate a simple trick to make the partitioning method more practically appealing for conference peer review. Finally, we complement our positive results with negative theoretical results where we prove that under various ways of strengthening the requirements, it is impossible for any algorithm to be strategyproof and efficient.

In the problem of adaptive compressed sensing, one wants to estimate an approximately $k$-sparse vector $x\in\mathbb{R}^n$ from $m$ linear measurements $A_1 x, A_2 x,\ldots, A_m x$, where $A_i$ can be chosen based on the outcomes $A_1 x,\ldots, A_{i-1} x$ of previous measurements. The goal is to output a vector $\hat{x}$ for which $$\|x-\hat{x}\|_p \le C \cdot \min_{k\text{-sparse } x'} \|x-x'\|_q\,$$ with probability at least $2/3$, where $C > 0$ is an approximation factor. Indyk, Price and Woodruff (FOCS'11) gave an algorithm for $p=q=2$ for $C = 1+\epsilon$ with $\Oh((k/\epsilon) \loglog (n/k))$ measurements and $\Oh(\log^*(k) \loglog (n))$ rounds of adaptivity. We first improve their bounds, obtaining a scheme with $\Oh(k \cdot \loglog (n/k) +(k/\epsilon) \cdot \loglog(1/\epsilon))$ measurements and $\Oh(\log^*(k) \loglog (n))$ rounds, as well as a scheme with $\Oh((k/\epsilon) \cdot \loglog (n\log (n/k)))$ measurements and an optimal $\Oh(\loglog (n))$ rounds. We then provide novel adaptive compressed sensing schemes with improved bounds for $(p,p)$ for every $0 < p < 2$. We show that the improvement from $O(k \log(n/k))$ measurements to $O(k \log \log (n/k))$ measurements in the adaptive setting can persist with a better $\epsilon$-dependence for other values of $p$ and $q$. For example, when $(p,q) = (1,1)$, we obtain $O(\frac{k}{\sqrt{\epsilon}} \cdot \log \log n \log^3 (\frac{1}{\epsilon}))$ measurements., Comment: To appear in ICALP 2018