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Traffic crashes profoundly impede traffic efficiency and pose economic challenges. Accurate prediction of post-crash traffic status provides essential information for evaluating traffic perturbations and developing effective solutions. Previous studies have established a series of deep learning models to predict post-crash traffic conditions, however, these correlation-based methods cannot accommodate the biases caused by time-varying confounders and the heterogeneous effects of crashes. The post-crash traffic prediction model needs to estimate the counterfactual traffic speed response to hypothetical crashes under various conditions, which demonstrates the necessity of understanding the causal relationship between traffic factors. Therefore, this paper presents the Marginal Structural Causal Transformer (MSCT), a novel deep learning model designed for counterfactual post-crash traffic prediction. To address the issue of time-varying confounding bias, MSCT incorporates a structure inspired by Marginal Structural Models and introduces a balanced loss function to facilitate learning of invariant causal features. The proposed model is treatment-aware, with a specific focus on comprehending and predicting traffic speed under hypothetical crash intervention strategies. In the absence of ground-truth data, a synthetic data generation procedure is proposed to emulate the causal mechanism between traffic speed, crashes, and covariates. The model is validated using both synthetic and real-world data, demonstrating that MSCT outperforms state-of-the-art models in multi-step-ahead prediction performance. This study also systematically analyzes the impact of time-varying confounding bias and dataset distribution on model performance, contributing valuable insights into counterfactual prediction for intelligent transportation systems., Comment: 13 pages, 9 figures

Adiabatic and non-adiabatic electron dynamics have been proposed to explain electron heating across collisionless shocks. We analyze the evolution of the suprathermal electrons across 310 quasi-perpendicular shocks with $1.7

We report a rare regime of Earth's magnetosphere interaction with sub-Alfv\'enic solar wind in which the windsock-like magnetosphere transforms into one with Alfv\'en wings. In the magnetic cloud of a Coronal Mass Ejection (CME) on April 24, 2023, NASA's Magnetospheric Multiscale mission distinguishes the following features: (1) unshocked and accelerated cold CME plasma coming directly against Earth's dayside magnetosphere; (2) dynamical wing filaments representing new channels of magnetic connection between the magnetosphere and foot points of the Sun's erupted flux rope; (3) cold CME ions observed with energized counter-streaming electrons, evidence of CME plasma captured due to reconnection between magnetic-cloud and Alfv\'en-wing field lines. The reported measurements advance our knowledge of CME interaction with planetary magnetospheres, and open new opportunities to understand how sub-Alfv\'enic plasma flows impact astrophysical bodies such as Mercury, moons of Jupiter, and exoplanets close to their host stars., Comment: 14 pages, including 4 figures, Under review in Geophys. Res. Lett

We use multi-spacecraft Magnetospheric Multiscale (MMS) observations to investigate electric fields and ion reflection at a non-stationary collisionless perpendicular plasma shock. We identify sub-proton scale (5-10 electron inertial lengths) large-amplitude normal electric fields, balanced by the Hall term ($\mathbf{J} \times \mathbf{B}/ne$), as a transient feature of the shock ramp related to non-stationarity (rippling). The associated electrostatic potential, comparable to the energy of the incident solar wind protons, decelerates incident ions and reflects a significant fraction of protons, resulting in more efficient shock-drift acceleration than a stationary planar shock., Comment: 14 pages, 4 figures, supplementary material

Solar Orbiter, a mission developed by the European Space Agency, explores in situ plasma across the inner heliosphere while providing remote-sensing observations of the Sun. Our study examines particle observations for the 30 October 2021 shock. The particles provide clear evidence of ion reflection up to several minutes upstream of the shock. Additionally, the magnetic and electric field observations contain complex electromagnetic structures near the shock, and we aim to investigate how they are connected to ion dynamics. The main goal of this study is to advance our understanding of the complex coupling between particles and the shock structure in high Mach number regimes of interplanetary shocks. We used observations of magnetic and electric fields, probe-spacecraft potential, and thermal and energetic particles to characterize the structure of the shock front and particle dynamics. Furthermore, ion velocity distribution functions were used to study reflected ions and their coupling to the shock. To determine shock parameters and study waves, we used several methods, including cold plasma theory, singular-value decomposition, minimum variance analysis, and shock Rankine-Hugoniot relations. To support the analysis and interpretation of the experimental data, test-particle analysis, and hybrid particle in-cell simulations were used. The ion velocity distribution functions show clear evidence of particle reflection in the form of backstreaming ions several minutes upstream. The shock structure has complex features at the ramp and whistler precursors. The backstreaming ions may be modulated by the complex shock structure, and the whistler waves are likely driven by gyrating ions in the foot. Supra-thermal ions up to 20 keV were observed, but shock-accelerated particles with energies above this were not.

Urban metro systems can provide highly efficient and effective movements of vast passenger volumes in cities, but they are often affected by disruptions, causing delays, crowding, and ultimately a decline in passenger satisfaction and patronage. To manage and mitigate such adverse consequences, metro operators could benefit greatly from a quantitative understanding of the causal impact of disruptions. Such information would allow them to predict future delays, prepare effective recovery plans, and develop real-time information systems for passengers on trip re-routing options. In this paper, we develop a performance evaluation tool for metro operators that can quantify the causal effects of service disruptions on passenger flows, journey times, travel speeds and crowding densities. Our modelling framework is simple to implement, robust to statistical sources of bias, and can be used with high-frequency large-scale smart card data (over 4.85 million daily trips in our case) and train movement data. We recover disruption effects at the points of disruption (e.g. at disrupted stations) as well as spillover effects that propagate throughout the metro network. This allows us to deliver novel insights on the spatio-temporal propagation of delays in densely used urban public transport networks. We find robust empirical evidence that the causal impacts of disruptions adversely affect service quality throughout the network, in ways that would be hard to predict absent a causal model.

The paper reviews methods that seek to draw causal inference from observational data and demonstrates how they can be applied to empirical problems in engineering research. It presents a framework for causal identification based on the concept of potential outcomes and reviews core contemporary methods that can be used to estimate causal quantities. The paper has two aims: first, to provide a consolidated overview of the statistical literature on causal inference for the data centric engineering community; and second, to illustrate how causal concepts and methods can be applied. The latter aim is achieved through Monte Carlo simulations designed to replicate typical empirical problems encountered in engineering research. R code for the simulations is made available for readers to run and adapt and citations are given to real world studies. Causal inference aims to quantify effects that occur due to explicit intervention (or 'treatment') in non-experimental settings, typically for non-randomly assigned treatments. The paper argues that analyses of engineering interventions are often characterized by such conditions, and consequently, that causal inference has immediate and valuable applicability.

Determination of the wave mode of short-wavelength electrostatic waves along with their generation mechanism requires reliable measurement of the wave electric field. We investigate the reliability of the electric field measurement for short-wavelength waves observed by MMS. We develop a method, based on spin-plane interferometry, to reliably determine the full 3D wave vector of the observed waves. We test the method on synthetic data and then apply it to ion acoustic wave bursts measured in situ in the solar wind. By studying the statistical properties of ion acoustic waves in the solar wind we retrieve the known results that the wave propagation is predominantly field-aligned. We also determine the wavelength of the waves. We find that the distribution peaks at around 100 m, which when normalized to the Debye length corresponds to scales between 10 and 20 Debye lengths.

The ability to reduce energy loss at semiconductor surfaces through passivation or surface field engineering has become an essential step in the manufacturing of efficient photovoltaic (PV) and optoelectronic devices. Similarly, surface modification of emerging halide perovskites with quasi-2D heterostructures is now ubiquitous to achieve PV power conversion efficiencies (PCEs) > 22% and has enabled single-junction PV devices to reach 25.7%, yet a fundamental understanding to how these treatments function is still generally lacking. This has established a bottleneck for maximizing beneficial improvements as no concrete selection and design rules currently exist. Here we uncover a new type of tunable passivation strategy and mechanism found in perovskite PV devices that were the first to reach the > 25% PCE milestone, which is enabled by surface treating a bulk perovskite layer with hexylammonium bromide (HABr). We uncover the simultaneous formation of an iodide-rich 2D layer along with a Br halide gradient achieved through partial halide exchange that extends from defective surfaces and grain boundaries into the bulk layer. We demonstrate and directly visualize the tunability of both the 2D layer thickness, halide gradient, and band structure using a unique combination of depth-sensitive nanoscale characterization techniques. We show that the optimization of this interface can extend the charge carrier lifetime to values > 30 {\mu}s, which is the longest value reported for a direct bandgap semiconductor (GaAs, InP, CdTe) over the past 50 years. Importantly, this work reveals an entirely new strategy and knob for optimizing and tuning recombination and charge transport at semiconductor interfaces and will likely establish new frontiers in achieving the next set of perovskite device performance records., Comment: Main text: 16 pages, 4 figures. Supporting Information: 47 pages, 26 figures, 6 tables

What can we hope to learn about brains from the free energy principle? In adopting the "primordial soup" physical model, Bruineberg et al. perpetuate the unsupported notion that the free energy principle has a meaningful physical--and neuronal--interpretation. We examine how minimization of free energy arises in physical contexts, and what this can and cannot tell us about brains., Comment: 3 pages, 0 figures

Whistler mode wave is a fundamental perturbation of electromagnetic fields and plasmas in various environments including planetary space, laboratory and astrophysics. The origin and evolution of the waves are a long-standing question due to the limited instrumental capability in resolving highly variable plasma and electromagnetic fields. Here, we analyse data with the high time resolution from the multi-scale magnetospheric spacecraft in the weak magnetic environment (i.e., foreshock) enabling a relatively long gyro-period of whistler mode wave. Moreover, we develop a novel approach to separate the three-dimensional fluctuating electron velocity distributions from their background, and have successfully captured the coherent resonance between electrons and electromagnetic fields at high frequency, providing the resultant growth rate of unstable whistler waves. Regarding the energy origin for the waves, the ion distributions are found to also play crucial roles in determining the eigenmode disturbances of fields and electrons. The quantification of wave growth rate can significantly advance the understandings of the wave evolution and the energy conversion with particles.

When analyzing plasma waves, a key parameter to determine is the phase velocity. It enables us to, for example, compute wavelengths, wave potentials, and determine the energy of resonant particles. The phase velocity of a wave, observed by a single spacecraft equipped with electric field probes, can be determined using interferometry techniques. While several methods have been developed to do this, they have not been documented in detail. In this study, we use an analytical model to analyze and compare three interferometry methods applied on the probe geometry of the Magnetospheric Multiscale spacecraft. One method relies on measured probe potentials, whereas the other two use different E-field measurements: one by reconstructing the E-field between two probes and the spacecraft, the other by constructing four pairwise parallel E-field components in the spacecraft spin-plane. We find that the potential method is sensitive both to how planar the wave is, and to spacecraft potential changes due to the wave. The E-field methods are less affected by the spacecraft potential, and while the reconstructed E-field method is applicable in some cases, the second E-field method is almost always preferable. We conclude that the potential based interferometry method is useful when spacecraft potential effects are negligible and the signals of the different probes are very well correlated. The method using two pairs of parallel E-fields is practically always preferable to the reconstructed E-field method and produces the correct velocity in the spin-plane, but it requires knowledge of the propagation direction to provide the full velocity., Comment: 35 pages, 9 figures, 1 table

The COVID-19 pandemic has drastically impacted people's travel behaviour and out-of-home activity participation. While countermeasures are being eased with increasing vaccination rates, the demand for public transport remains uncertain. To investigate user preferences to travel by London Underground during the pandemic, we conducted a stated choice experiment among its pre-pandemic users (N=961). We analysed the collected data using multinomial and mixed logit models. Our analysis provides insights into the sensitivity of the demand for the London Underground with respect to travel attributes (crowding density and travel time), the epidemic situation (confirmed new COVID-19 cases), and interventions (vaccination rates and mandatory face masks). Mandatory face masks and higher vaccination rates are the top two drivers of travel demand for the London Underground during COVID-19. The positive impact of vaccination rates on the Underground demand increases with crowding density, and the positive effect of mandatory face masks decreases with travel time. Mixed logit reveals substantial preference heterogeneity. For instance, while the average effect of mandatory face masks is positive, preferences of around 20% of the pre-pandemic users to travel by the Underground are negatively affected. The estimated demand sensitivities are relevant for supply-demand management in transit systems and the calibration of advanced epidemiological models.

The fundamental relationship of traffic flow is empirically estimated by fitting a regression curve to a cloud of observations of traffic variables. Such estimates, however, may suffer from the confounding/endogeneity bias due to omitted variables such as driving behaviour and weather. To this end, this paper adopts a causal approach to obtain an unbiased estimate of the fundamental flow-density relationship using traffic detector data. In particular, we apply a Bayesian non-parametric spline-based regression approach with instrumental variables to adjust for the aforementioned confounding bias. The proposed approach is benchmarked against standard curve-fitting methods in estimating the flow-density relationship for three highway bottlenecks in the United States. Our empirical results suggest that the saturated (or hypercongested) regime of the estimated flow-density relationship using correlational curve fitting methods may be severely biased, which in turn leads to biased estimates of important traffic control inputs such as capacity and capacity-drop. We emphasise that our causal approach is based on the physical laws of vehicle movement in a traffic stream as opposed to a demand-supply framework adopted in the economics literature. By doing so, we also aim to conciliate the engineering and economics approaches to this empirical problem. Our results, thus, have important implications both for traffic engineers and transport economists.

As the field of connectomics has matured, it has expanded from mapping the existence of connections between brain components to measuring the strength of connections. This information is increasingly accessible via methodologies such as pairing functional magnetic resonance (MR) imaging and MR tractography in the same human subject, as well as novel methods in non-human animals using optogenetics. Systems and network neuroscience have in recent years focused extensively on explaining correlation patterns of functional activity in the brain in terms of the degree of connectedness of brain components, the so-called functional connectivity-structural connectivity relationship (SC-FC). What has been surprising has been how low the SC-FC correlations are. Why is it that brain parts that are more well-connected appear not to engender more correlated activity between them? Several explanations have been proposed but one possibility has not been considered: perhaps more neural activity doesn't imply more functional involvement. This article examines this possibility and proposes a new general framework for understanding brain network dynamics based on the design constraints of large-scale network communication systems. With this new perspective, we may start to answer the article's main question, and perhaps others.

In the usual Bayesian setting, a full probabilistic model is required to link the data and parameters, and the form of this model and the inference and prediction mechanisms are specified via de Finetti's representation. In general, such a formulation is not robust to model mis-specification of its component parts. An alternative approach is to draw inference based on loss functions, where the quantity of interest is defined as a minimizer of some expected loss, and to construct posterior distributions based on the loss-based formulation; this strategy underpins the construction of the Gibbs posterior. We develop a Bayesian non-parametric approach; specifically, we generalize the Bayesian bootstrap, and specify a Dirichlet process model for the distribution of the observables. We implement this using direct prior-to-posterior calculations, but also using predictive sampling. We also study the assessment of posterior validity for non-standard Bayesian calculations, and provide an efficient way to calibrate the scaling parameter in the Gibbs posterior so that it can achieve the desired coverage rate. We show that the developed non-standard Bayesian updating procedures yield valid posterior distributions in terms of consistency and asymptotic normality under model mis-specification. Simulation studies show that the proposed methods can recover the true value of the parameter efficiently and achieve frequentist coverage even when the sample size is small. Finally, we apply our methods to evaluate the causal impact of speed cameras on traffic collisions in England.

Consumer preference elicitation is critical to devise effective policies for the diffusion of electric vehicles (EVs) in India. This study contributes to the EV demand literature in the Indian context by (a) analysing the EV attributes and attitudinal factors of Indian car buyers that determine consumers' preferences for EVs, (b) estimating Indian consumers' willingness to pay (WTP) to buy EVs with improved attributes, and c) quantifying how the reference dependence affects the WTP estimates. We adopt a hybrid choice modelling approach for the above analysis. The results indicate that accounting for reference dependence provides more realistic WTP estimates than the standard utility estimation approach. Our results suggest that Indian consumers are willing to pay an additional USD 10-34 in the purchase price to reduce the fast charging time by 1 minute, USD 7-40 to add a kilometre to the driving range of EVs at 200 kilometres, and USD 104-692 to save USD 1 per 100 kilometres in operating cost. These estimates and the effect of attitudes on the likelihood to adopt EVs provide insights about EV design, marketing strategies, and pro-EV policies (e.g., specialised lanes and reserved parking for EVs) to expedite the adoption of EVs in India.

Congestion; operational delays due to a vicious circle of passenger-congestion and train-queuing; is an escalating problem for metro systems because it has negative consequences from passenger discomfort to eventual mode-shifts. Congestion arises due to large volumes of passenger boardings and alightings at bottleneck stations, which may lead to increased stopping times at stations and consequent queuing of trains upstream, further reducing line throughput and implying an even greater accumulation of passengers at stations. Alleviating congestion requires control strategies such as regulating the inflow of passengers entering bottleneck stations. The availability of large-scale smartcard and train movement data from day-to-day operations facilitates the development of models that can inform such strategies in a data-driven way. In this paper, we propose to model station-level passenger-congestion via empirical passenger boarding-alightings and train flow relationships, henceforth, fundamental diagrams (FDs). We emphasise that estimating FDs using station-level data is empirically challenging due to confounding biases arising from the interdependence of operations at different stations, which obscures the true sources of congestion in the network. We thus adopt a causal statistical modelling approach to produce FDs that are robust to confounding and as such suitable to properly inform control strategies. The closest antecedent to the proposed model is the FD for road traffic networks, which informs traffic management strategies, for instance, via locating the optimum operation point. Our analysis of data from the Mass Transit Railway, Hong Kong indicates the existence of concave FDs at identified bottleneck stations, and an associated critical level of boarding-alightings above which congestion sets-in unless there is an intervention.

Whistler waves are thought to play an essential role in the dynamics of collisionless shocks. We use the magnetospheric multiscale (MMS) spacecraft to study whistler waves around the lower hybrid frequency, upstream of 11 quasi-perpendicular super-critical shocks. We apply the 4-spacecraft timing method to unambiguously determine the wave vector $\mathbf{k}$ of whistler waves. We find that the waves are oblique to the background magnetic field with a wave-normal angle between $20^{\circ}$ and $42^{\circ}$, a wavelength around 100 km which is close to the ion inertial length. We also find that $\mathbf{k}$ is predominantly in the same plane as the magnetic field and the normal to the shock. By combining this precise knowledge of $\mathbf{k}$ with high-resolution measurements of the 3D ion velocity distribution we show that a reflected ion beam is in resonance with the waves, opening up the possibility for wave-particle interaction between the reflected ions and the observed whistlers. The linear stability analysis of a system mimicking the observed distribution, suggests that such a system can produce the observed waves.

Compressive plasma turbulence is investigated at sub-ion scales in the solar wind using both the Fast Plasma Investigation (FPI) instrument on the Magnetospheric MultiScale mission (MMS), as well as using calibrated spacecraft potential data from the Spin Plane Double Probe (SDP) instrument. The data from FPI allow a measurement down to the sub-ion scale region ($f_{sc}\gtrsim 1$ Hz) to be investigated before the instrumental noise becomes significant at a spacecraft frame frequency of $f_{sc}\approx 3$Hz, whereas calibrated spacecraft potential allows a measurement up to $f_{sc}\approx 40$Hz. In this work, we give a detailed description of density estimation in the solar wind using the spacecraft potential measurement from the SDP instrument on MMS. Several intervals of solar wind plasma have been processed using the methodology described which are made available. One of the intervals is investigated in more detail and the power spectral density of the compressive fluctuations is measured from the inertial range to the sub-ion range. The morphology of the density spectra can be explained by either a cascade of Alfv\'en waves and slow waves at large scales and kinetic Alfv\'en waves at sub-ion scales, or more generally by the Hall effect. Using electric field measurements the two hypotheses are discussed., Comment: Accepted to APJS

Transit operators need vulnerability measures to understand the level of service degradation under disruptions. This paper contributes to the literature with a novel causal inference approach for estimating station-level vulnerability in metro systems. The empirical analysis is based on large-scale data on historical incidents and population-level passenger demand. This analysis thus obviates the need for assumptions made by previous studies on human behaviour and disruption scenarios. We develop four empirical vulnerability metrics based on the causal impact of disruptions on travel demand, average travel speed and passenger flow distribution. Specifically, the proposed metrics based on the irregularity in passenger flow distribution extends the scope of vulnerability measurement to the entire trip distribution, instead of just analysing the disruption impact on the entry or exit demand (that is, moments of the trip distribution). The unbiased estimates of disruption impact are obtained by adopting a propensity score matching method, which adjusts for the confounding biases caused by non-random occurrence of disruptions. An application of the proposed framework to the London Underground indicates that the vulnerability of a metro station depends on the location, topology, and other characteristics. We find that, in 2013, central London stations are more vulnerable in terms of travel demand loss. However, the loss of average travel speed and irregularity in relative passenger flows reveal that passengers from outer London stations suffer from longer individual delays due to lack of alternative routes.

Spatial count data models are used to explain and predict the frequency of phenomena such as traffic accidents in geographically distinct entities such as census tracts or road segments. These models are typically estimated using Bayesian Markov chain Monte Carlo (MCMC) simulation methods, which, however, are computationally expensive and do not scale well to large datasets. Variational Bayes (VB), a method from machine learning, addresses the shortcomings of MCMC by casting Bayesian estimation as an optimisation problem instead of a simulation problem. Considering all these advantages of VB, a VB method is derived for posterior inference in negative binomial models with unobserved parameter heterogeneity and spatial dependence. P\'olya-Gamma augmentation is used to deal with the non-conjugacy of the negative binomial likelihood and an integrated non-factorised specification of the variational distribution is adopted to capture posterior dependencies. The benefits of the proposed approach are demonstrated in a Monte Carlo study and an empirical application on estimating youth pedestrian injury counts in census tracts of New York City. The VB approach is around 45 to 50 times faster than MCMC on a regular eight-core processor in a simulation and an empirical study, while offering similar estimation and predictive accuracy. Conditional on the availability of computational resources, the embarrassingly parallel architecture of the proposed VB method can be exploited to further accelerate its estimation by up to 20 times.

Crowding valuation of subway riders is an important input to various supply-side decisions of transit operators. The crowding cost perceived by a transit rider is generally estimated by capturing the trade-off that the rider makes between crowding and travel time while choosing a route. However, existing studies rely on static compensatory choice models and fail to account for inertia and the learning behaviour of riders. To address these challenges, we propose a new dynamic latent class model (DLCM) which (i) assigns riders to latent compensatory and inertia/habit classes based on different decision rules, (ii) enables transitions between these classes over time, and (iii) adopts instance-based learning theory to account for the learning behaviour of riders. We use the expectation-maximisation algorithm to estimate DLCM, and the most probable sequence of latent classes for each rider is retrieved using the Viterbi algorithm. The proposed DLCM can be applied in any choice context to capture the dynamics of decision rules used by a decision-maker. We demonstrate its practical advantages in estimating the crowding valuation of an Asian metro's riders. To calibrate the model, we recover the daily route preferences and in-vehicle crowding experiences of regular metro riders using a two-month-long smart card and vehicle location data. The results indicate that the average rider follows the compensatory rule on only 25.5% of route choice occasions. DLCM estimates also show an increase of 47% in metro riders' valuation of travel time under extremely crowded conditions relative to that under uncrowded conditions.

Transport operators have a range of intervention options available to improve or enhance their networks. Such interventions are often made in the absence of sound evidence on resulting outcomes. Cycling superhighways were promoted as a sustainable and healthy travel mode, one of the aims of which was to reduce traffic congestion. Estimating the impacts that cycle superhighways have on congestion is complicated due to the non-random assignment of such intervention over the transport network. In this paper, we analyse the causal effect of cycle superhighways utilising pre-intervention and post-intervention information on traffic and road characteristics along with socio-economic factors. We propose a modeling framework based on the propensity score and outcome regression model. The method is also extended to the doubly robust set-up. Simulation results show the superiority of the performance of the proposed method over existing competitors. The method is applied to analyse a real dataset on the London transport network. The methodology proposed can assist in effective decision making to improve network performance.

Magnetic reconnection (MR) and the associated concurrently occurring waves have been extensively studied at large-scale plasma boundaries, in quasi-symmetric and asymmetric configurations in the terrestrial magnetotail and at the magnetopause. Recent high-resolution observations by MMS (Magnetospheric Multiscale) spacecraft indicate that MR can occur also in the magnetosheath where the conditions are highly turbulent when the upstream shock geometry is quasi-parallel. The strong turbulent motions make the boundary conditions for evolving MR complicated. In this paper it is demonstrated that the wave observations in localized regions of MR can serve as an additional diagnostic tool reinforcing our capacity for identifying MR events in turbulent plasmas. It is shown that in a close resemblance with MR at large-scale boundaries, turbulent reconnection associated whistler waves occur at separatrix/outflow regions and at the outer boundary of the electron diffusion region, while lower hybrid drift waves are associated with density gradients during the crossing of the current sheet. The lower hybrid drift instability can make the density inhomogeneities rippled. The identification of MR associated waves in the magnetosheath represents also an important milestone for developing a better understanding of energy redistribution and dissipation in turbulent plasmas.

Wave function (WF) in density functional theory (DFT) embedding methods provide a framework for performing localized, high accuracy WF calculations on a system, while not incurring the full computational cost of the WF calculation on the full system. In order to effectively partition a system into localized WF and DFT subsystems, we utilize the Huzinaga level-shift projection operator within an absolutely localized basis. In this work, we study the ability of the absolutely localized Huzinaga level-shift projection operator method to study complex WF and DFT partitions, including partitions between multiple covalent bonds, a double bond, and transition metal-ligand bonds. We find that our methodology can accurately describe all of these complex partitions. Additionally, we study the robustness of this method with respect to the WF method, specifically where the embedded systems were described using a multiconfigurational WF method. We found that the method is systematically improvable with respect to both the number of atoms in the WF region and the size of the basis set used, with energy errors less than 1 kcal/mol. Additionally, we calculated the adsorption energy of H$_2$ to a model of an iron metal organic framework (Fe-MOF-74) to within 1 kcal/mol compared to CASPT2 calculations performed on the full model while incurring only a small fraction of the full computational cost. This work demonstrates that the absolutely localized Huzinaga level-shift projection operator method is applicable to very complex systems with difficult electronic structures., Comment: 33 pages, 8 figures