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Ensemble Kalman inversion (EKI) is a derivative-free, particle-based optimization method for solving inverse problems. It can be shown that EKI approximates a gradient flow, which allows the application of methods for accelerating gradient descent. Here, we show that Nesterov acceleration is effective in speeding up the reduction of the EKI cost function on a variety of inverse problems. We also implement Nesterov acceleration for two EKI variants, unscented Kalman inversion and ensemble transform Kalman inversion. Our specific implementation takes the form of a particle-level nudge that is demonstrably simple to couple in a black-box fashion with any existing EKI variant algorithms, comes with no additional computational expense, and with no additional tuning hyperparameters. This work shows a pathway for future research to translate advances in gradient-based optimization into advances in gradient-free Kalman optimization.

The impact of several $``\text{flavours}"$ of free-stream turbulence (FST) on the structural response of a cantilevered cylinder, subjected to a turbulent cross-flow is investigated. At high enough Reynolds numbers, the cylinder generates a spectrally rich turbulent wake which significantly contributing to the experienced loads. The presence of FST introduces additional complexity through two primary mechanisms: $\textbf{directly}$, by imposing a fluctuating velocity field on the cylinder's surface, and $\textbf{indirectly}$, by altering the vortex shedding dynamics, modifying the experienced loads. We employ concurrent temporally resolved Particle Image Velocimetry (PIV) and distributed strain measurements using Rayleigh backscattering fibre optic sensors (RBS) to instrument the surrounding velocity field and the structural strain respectively. By using various turbulence-generating grids, and manipulating their distance to the cylinder, we assess a broad FST parameter space allowing us to individually explore the influence of transverse integral length scale ($\mathcal{L}_{13}/D$), and turbulence intensity ($TI$) of the FST on the developing load dynamics. The presence of FST enhances the magnitude of the loads acting on the cylinder. This results from a decreased vortex formation length, increased coherence of regular vortex shedding, and energy associated with this flow structure in the near-wake. The cylinder's structural response is mainly driven by the vortex shedding dynamics, and their modification induced by the presence of FST, ie. the indirect effect outweighs the direct effect. From the explored FST parameter space, $TI$ was seen to be the main driver of enhanced loading conditions, presenting a positive correlation with the fluctuating loads magnitude at the root.

Jupiter's Great Red Spot (GRS) was mapped by the James Webb Space Telescope (JWST)/Mid-Infrared Instrument (4.9-27.9 micron) in July and August 2022. These observations took place alongside a suite of visual and infrared observations from; Hubble, JWST/NIRCam, Very Large Telescope/VISIR and amateur observers which provided both spatial and temporal context across the jovian disc. The stratospheric temperature structure retrieved using the NEMESIS software revealed a series of hot-spots above the GRS. These could be the consequence of GRS-induced wave activity. In the troposphere, the temperature structure was used to derive the thermal wind structure of the GRS vortex. These winds were only consistent with the independently determined wind field by JWST/NIRCam at 240 mbar if the altitude of the Hubble-derived winds were located around 1,200 mbar, considerably deeper than previously assumed. No enhancement in ammonia was found within the GRS but a link between elevated aerosol and phosphine abundances was observed within this region. North-south asymmetries were observed in the retrieved temperature, ammonia, phosphine and aerosol structure, consistent with the GRS tilting in the north-south direction. Finally, a small storm was captured north-west of the GRS that displayed a considerable excess in retrieved phosphine abundance, suggestive of vigorous convection. Despite this, no ammonia ice was detected in this region. The novelty of JWST required us to develop custom-made software to resolve challenges in calibration of the data. This involved the derivation of the "FLT-5" wavelength calibration solution that has subsequently been integrated into the standard calibration pipeline., Comment: 53 pages, 19 figures, 4 tables

Randomized algorithms exploit stochasticity to reduce computational complexity. One important example is random feature regression (RFR) that accelerates Gaussian process regression (GPR). RFR approximates an unknown function with a random neural network whose hidden weights and biases are sampled from a probability distribution. Only the final output layer is fit to data. In randomized algorithms like RFR, the hyperparameters that characterize the sampling distribution greatly impact performance, yet are not directly accessible from samples. This makes optimization of hyperparameters via standard (gradient-based) optimization tools inapplicable. Inspired by Bayesian ideas from GPR, this paper introduces a random objective function that is tailored for hyperparameter tuning of vector-valued random features. The objective is minimized with ensemble Kalman inversion (EKI). EKI is a gradient-free particle-based optimizer that is scalable to high-dimensions and robust to randomness in objective functions. A numerical study showcases the new black-box methodology to learn hyperparameter distributions in several problems that are sensitive to the hyperparameter selection: two global sensitivity analyses, integrating a chaotic dynamical system, and solving a Bayesian inverse problem from atmospheric dynamics. The success of the proposed EKI-based algorithm for RFR suggests its potential for automated optimization of hyperparameters arising in other randomized algorithms.

The thermal conductivity of water features a maximum (TCM) as a function of temperature at constant pressure. By examining why molecular force fields succeed or fail to reproduce the maximum and interpreting our results using the Bridgman equation, we show that water's TCM is connected with its compressibility minimum. Using Stillinger-Weber potentials for tetrahedral liquids, we interpolate between the behaviour of simple liquids and highly tetrahedral materials such as carbon. Together with two vanishing limits at low/high tetrahedrality, we identify three regimes for the TCM: when it originates from either the compressibility minimum or density maximum, or both. Thus, the TCM exists in a "Goldilocks Zone" of tetrahedral order. We provide a thermodynamic explanation for the TCM of not only water, but tetrahedral liquids in general.

Machine learning is playing an increasing role in hydrology, supplementing or replacing physics-based models. One notable example is the use of recurrent neural networks (RNNs) for forecasting streamflow given observed precipitation and geographic characteristics. Training of such a model over the continental United States (CONUS) has demonstrated that a single set of model parameters can be used across independent catchments, and that RNNs can outperform physics-based models. In this work, we take a next step and study the performance of RNNs for river routing in land surface models (LSMs). Instead of observed precipitation, the LSM-RNN uses instantaneous runoff calculated from physics-based models as an input. We train the model with data from river basins spanning the globe and test it using historical streamflow measurements. The model demonstrates skill at generalization across basins (predicting streamflow in catchments not used in training) and across time (predicting streamflow during years not used in training). We compare the predictions from the LSM-RNN to an existing physics-based model calibrated with a similar dataset and find that the LSM-RNN outperforms the physics-based model: a gain in median NSE from 0.56 to 0.64 (time-split experiment) and from 0.30 to 0.34 (basin-split experiment). Our results show that RNNs are effective for global streamflow prediction from runoff inputs and motivate the development of complete routing models that can capture nested sub-basis connections., Comment: 32 pages, 11 figures; submitted in HESS (EGU) with CCBY license

In this work we investigate the spatio-temporal nature of various coherent modes present in a rotor wake using a combination of new PIV experiments and data from Biswas and Buxton (2024). A multi-scale triple decomposition of the acquired velocity field is sought to extract the coherent modes and thereafter, the energy exchanges to and from them are studied using the multi-scale triple-decomposed coherent kinetic energy budgets developed by Baj and Buxton (2017). Different frequencies forming the tip vortex system (such as the blade passing frequency, turbine's rotational frequency and their harmonics) are found to be energised by different sources such as production from the mean flow or non-linear triadic interaction or both, similar to the primary, secondary or the mixed modes discussed in Biswas et al. (2022). In fact, the tip vortex system forms a complex network of nonlinear triadic energy transfers, the nature and the magnitudes of which depend on \lambda. On the other hand, the modes associated with the sheddings from the nacelle or tower and wake meandering are found to be primarily energised by the mean flow. We show that the tip vortex system exchanges energy with the mean flow primarily through the turbine's rotational frequency. In fact, the system transfers energy back to the mean flow through the turbine's rotational frequency at some distance downstream marking the onset location of wake recovery (x_{wr}). x_{wr} is shown to reduce with \lambda due to stronger interaction and earlier merging of the tip vortices at a higher \lambda.

We performed the temperature diagnostics using inversions of data from nine spectroscopic observations obtained with the IRIS spectrograph in the MgII h & k lines. The sensitivity to the temperature of the emission peaks of these lines was exploited to determine the temperature of the coronal rain plasma using inversions of the spectroscopic profiles. Additional relationships between different spectral features of these lines, derived from the use of 3D radiative transfer line synthesis applied to simulations, were employed in order to derive the line-of-sight (LoS) velocities in different parts of the coronal rain plasma. For the first time, spectroscopic inversions of coronal rain were successfully performed. Temperatures derived from the inversions yield coronal rain clump temperatures at the formation height of the emission peaks of the MgII h & k lines in the range between 5000 and 7000 K. This narrow range of values remains consistent among all the different observations used in this work. We obtained LoS velocities of up to 40 km/s, which are consistent with the motion of the plasma being mostly constrained to the plane of the sky, as the coronal rain was mostly detected shortly after its formation and the observations took place in the disc. Furthermore, velocity diagnostics led to the detection of larger velocities at higher layers of the coronal rain plasma in some cases. This increased velocity seems to indicate that at some point (at least) during the fall of coronal rain clumps towards the chromosphere, the material in the upper part of the coronal rain plasma is falling with greater velocity than the material below it. The conditions of the temperature and density of the coronal rain plasma where the Mg II h line forms appear to be slightly different that those of the Mg II k line, with the former found at slightly colder and denser parts of the plasma.

Saturn's northern summertime hemisphere was mapped by JWST/MIRI (4.9-27.9 $\mu$m) in November 2022, tracing the seasonal evolution of temperatures, aerosols, and chemical species in the five years since the end of the Cassini mission. The spectral region between reflected sunlight and thermal emission (5.1-6.8 $\mu$m) is mapped for the first time, enabling retrievals of phosphine, ammonia, and water, alongside a system of two aerosol layers (an upper tropospheric haze $p<0.3$ bars, and a deeper cloud layer at 1-2 bars). Ammonia displays substantial equatorial enrichment, suggesting similar dynamical processes to those found in Jupiter's equatorial zone. Saturn's North Polar Stratospheric Vortex has warmed since 2017, entrained by westward winds at $p<10$ mbar, and exhibits localised enhancements in several hydrocarbons. The strongest latitudinal temperature gradients are co-located with the peaks of the zonal winds, implying wind decay with altitude. Reflectivity contrasts at 5-6 $\mu$m compare favourably with albedo contrasts observed by Hubble, and several discrete vortices are observed. A warm equatorial stratospheric band in 2022 is not consistent with a 15-year repeatability for the equatorial oscillation. A stacked system of windshear zones dominates Saturn's equatorial stratosphere, and implies a westward equatorial jet near 1-5 mbar at this epoch. Lower stratospheric temperatures, and local minima in the distributions of several hydrocarbons, imply low-latitude upwelling and a reversal of Saturn's interhemispheric circulation since equinox. Latitudinal distributions of stratospheric ethylene, benzene, methyl and carbon dioxide are presented for the first time, and we report the first detection of propane bands in the 8-11 $\mu$m region., Comment: 53 pages, 25 figures, accepted for publication in JGR: Planets

The near wake of a small-scale wind turbine is investigated using Particle Image Velocimetry (PIV) experiments at different tip speed ratios ($\lambda$). The wind turbine model had a nacelle and a tower mimicking real scale wind turbines. The near wake is found to be dominated by multiple coherent structures including the tip vortices, distinct vortex sheddings from the nacelle and tower, and wake meandering. The merging of the tip vortices is found to be strongly dependent on $\lambda$. A convective length scale ($L_c$) related to the pitch of the helical vortices is defined which is shown to be a better length scale than turbine diameter ($D$) to demarcate the near wake from the far wake. The tower induced strong vertical asymmetry in the flow by destabilising the tip vortices and promoting mixing in the lower (below the nacelle) plane. The nacelle's shedding is found to be important in 'seeding' wake meandering which although not potent, exists close to the nacelle, and it becomes important only after a certain distance downstream ($x>3L_c$). A link between the 'effective porosity' of the turbine and $\lambda$ is established and the strength and frequency of wake meandering is found to be dependent on $\lambda$. In fact, a decreasing trend of wake meandering frequency with $\lambda$ is observed, similar to vortex shedding from a porous disk at varying porosity. Such similarity upholds the notion of wake meandering being a global instability of the turbine, which can be considered as a 'porous' bluff body of diameter $D$.

Context. Chromospheric fibrils are thin and elongated structures that connect nearby photospheric magnetic field concentrations of opposite polarities. Aims. We assess the possibilities and drawbacks related to the use of current instrumentation and inversion techniques to infer the thermodynamic structure of chromospheric fibrils. Methods. We employed spectroscopic observations obtained in the Ca ii 854.2 nm line with the CRISP instrument at the Swedish 1-m Solar Telescope and in coordination with observations in the ultraviolet Mg ii h & k lines taken with the IRIS satellite. We studied the temperature sensitivity of these chromospheric lines to properly invert their spectral profiles with the Stockholm inversion Code and determine the temperature, line-of-sight velocity, and microturbulent velocity of manually traced chromospheric fibrils present in the field of view. Results. Fibril-like structures show a very particular dependence of their temperature as a function of the position along their length. Their temperatures at the detected footpoints are, on average, 300 K higher than the temperature at the midpoint. The temperature variation appears to be almost symmetrical in shape, with partially traced fibrils showing a similar trend for the temperature variation. Additionally, the response of the Ca ii 854.2 nm line core to variations of the temperature for the inverted models of the atmosphere in fibril areas seems to be insufficient to properly resolve the aforementioned temperature structure. Only the addition of more temperature sensitive lines such as the Mg ii h & k lines would make it possible to properly infer the thermodynamic properties of chromospheric fibrils. Comparisons between the results obtained here and in previous studies focused on bright Ca ii K fibrils yield great similarities between these structures in terms of their temperature.

The effect of freestream turbulence on the spreading of the near wake of a circular cylinder is investigated through particle image velocimetry (PIV) data. Different ``flavours'' of freestream turbulence, in which the turbulence intensity and integral length scale are independently varied, are subjected to the cylinder. The time-averaged spreading of the near wake is decoupled into the growth through entrainment and the envelope of the spatial extent of the instantaneous wake due to wake ``meandering'', induced by the presence of large-scale coherent structures, i.e. the von Karman vortex street. Unlike for the far field of a turbulent wake, examined by Kankanwadi and Buxton (2020), it is shown that freestream turbulence enhances the entrainment rate into the wake in comparison to a non-turbulent background. Both the turbulence intensity and the integral length scale of the background turbulence are important in this regard, contrasting to the far wake where only the turbulence intensity is important. Additionally, wake meandering is enhanced by the presence of background turbulence, and here the integral length scale is the dominant parameter. Combining these findings yields the oft-reported result that background turbulence enhances the time-averaged near-wake growth rate. The influence of wake meandering is isolated by conducting similar experiments in which a splitter plate is mounted to the rear face of the cylinder, thereby eliminating the von Karman vortex street. These results show that when large-scale vortices aren't present within the turbulent wake then freestream turbulence actually suppresses the entrainment rate, relative to a non-turbulent background, in results that mirror Kankanwadi and Buxton (2020). We therefore postulate that freestream turbulence has the effect to enhance large-scale entrainment via engulfment, but suppress entrainment via small-scale nibbling., Comment: 26 pages, 19 figures, submitted to Physical Review Fluids

This study aims to examine the spatial evolution of the geometrical features of the turbulent/turbulent interface (TTI) in a cylinder wake. The wake is exposed to various turbulent backgrounds in which the turbulence intensity and the integral length scale are independently varied and comparisons to a turbulent/non-turbulent interface (TNTI) are drawn. The turbulent wake was marked with a high-Schmidt-number ($Sc$) scalar and a planar laser induced fluorescence (PLIF) experiment was carried out to capture the interface between the wake and the ambient flow from $x/d$ = 5 to 40 where $x$ is the streamwise coordinate from the centre of the cylinder and $d$ is the cylinder's diameter. It is found that the TTI generally spreads faster toward the ambient flow than the TNTI. A transition region of the interfaces' spreading is found at $x/d \approx 15$, after which the interfaces propagate at a slower rate than previously (upstream) and the mean interface positions of both TNTI and TTI scale with the local wake half-width. The location of both the TNTI and TTI have non-Gaussian probability density functions (PDFs) in the near wake because of the influence of the large-scale coherent motions present within the flow. Further downstream, after the large-scale coherent motions have dissipated, the TNTI position PDF does become Gaussian. For the first time we explore the spatial variation of the ``roughness'' of the TTI, quantified via the fractal dimension, from near field to far field. The length scale in the background flow has a profound effect on the TTI fractal dimension in the near wake, whilst the turbulence intensity only becomes important for the fractal dimension farther downstream.

We study off-limb emission of the lower solar atmosphere using high-resolution imaging spectroscopy in the H$\beta$ and Ca II 8542 \r{A} lines obtained with the CHROMospheric Imaging Spectrometer (CHROMIS) and the CRisp Imaging SpectroPolarimeter (CRISP) on the Swedish 1-m Solar Telescope. The H$\beta$ line wing images show the dark intensity gap between the photospheric limb and chromosphere which is absent in the Ca II images. We calculate synthetic spectra of the off-limb emissions with the RH code in the one-dimension spherical geometry and find good agreement with the observations. The analysis of synthetic line profiles shows that the gap in the H$\beta$ line wing images maps the temperature minimum region between the photosphere and chromosphere due to the well known opacity and emissivity gap of Balmer lines in this layer. However, observed gap is detected farther from the line core in the outer line wing positions than in the synthetic profiles. We found that an increased microturbulence in the model chromosphere is needed to reproduce the dark gap in the outer line wing, suggesting that observed H$\beta$ gap is the manifestation of the temperature minimum and the dynamic nature of the solar chromosphere. The temperature minimum produces a small enhancement in synthetic Ca II line-wing intensities. Observed off-limb Ca II line-wing emissions show similar enhancement below temperature minimum layer near the edge of the photospheric limb., Comment: 14 pages, 8 figures, accepted in ApJ

Temperature gradients induce mass separation in mixtures in a process called thermodiffusion and quantified by the Soret coefficient. The existence of minima in the Soret coefficient of aqueous solutions was controversial until fairly recently, where a combination of experiments and simulations provided evidence for the existence of this physical phenomenon. However, the physical origin of the minima and more importantly its generality, e.g. in non-aqueous liquid mixtures, is still an outstanding question. We report the existence of a minimum in liquid mixtures of non-polar liquids modelled as Lennard-Jones mixtures, demonstrating the generality of this phenomenon. The Soret coefficient minimum originates from a coincident minimum in the thermodynamic factor, and hence denotes a maximimzation of non-ideality mixing conditions. We explain the microscopic origin of this effect in terms of the atomic coordination structure of the mixtures.

This paper discusses the statistical inference problem associated with testing for dependence between two continuous random variables using Kendall's $\tau$ in the context of the missing data problem. We prove the worst-case identified set for this measure of association always includes zero. The consequence of this result is that robust inference for dependence using Kendall's $\tau$, where robustness is with respect to the form of the missingness-generating process, is impossible., Comment: 15 Pages

The heliophysics catalogues published by the Ebro Observatory during 1910--1937 have been converted into a digital format in order to provide the data for computational processing. This has allowed us to study in detail the North-South (N-S) asymmetry of solar activity in that period, focusing on two different structures located at two different layers of the solar atmosphere: sunspots (Photosphere) and solar plages (Chromosphere). The examination of the absolute and normalised N-S asymmetry indices in terms of their monthly sum of occurrences and areas has made possible to find out a cyclic behaviour in the solar activity, in which the preferred hemisphere changes systematically with a global period of 7.9 $\pm$ 0.2 yr. In order to verify and quantify accurately this periodicity and study its prevalence in time, we employed the RGO-USAF/NOAA sunspot data series during 1874--2016. Then, we examined each absolute asymmetry index time series through different techniques as the power spectrum analysis, the Complete Ensemble Empirical Mode Decomposition With Adaptive Noise algorithm, or the Morlet wavelet transform. The combined results reveal a cyclic behaviour at different time scales, consisting in two quite stable periodicities of 1.47 $\pm$ 0.02 yr and 3.83 $\pm$ 0.06 yr, which coexist with another three discontinuous components with more marked time-varying periods with means of 5.4 $\pm$ 0.2 yr, 9.0 $\pm$ 0.2 yr, and 12.7 $\pm$ 0.3 yr. Moreover, during 1910--1937, only two dominant signals with averaged periods of 4.10 $\pm$ 0.04 yr and 7.57 $\pm$ 0.03 yr can be clearly observed. Finally, in both signals, periods are slightly longer for plages in comparison with sunspots., Comment: 18 pages, 8 figures, 14 tables

Coronal holes and active regions are typical magnetic structures found in the solar atmosphere. We propose several magnetohydrostatic equilibrium solutions that are representative of these structures in two dimensions. Our models include the effect of a finite plasma-$\beta$ and gravity, but the distinctive feature is that we incorporate a thermal structure with properties similar to those reported by observations. We developed a semi-analytical method to compute the equilibrium configuration. Using this method, we obtain cold and under-dense plasma structures in open magnetic fields representing coronal holes, while in closed magnetic configurations, we achieve the characteristic hot and over-dense plasma arrangements of active regions. Although coronal holes and active regions seem to be antagonistic structures, we find that they can be described using a common thermal structure that depends on the flux function. In addition to the force balance, the energy balance is included in the constructed models using an a posteriori approach. From the two-dimensional computation of thermal conduction and radiative losses in our models, we infer the required heating function to achieve energy equilibrium. We find that the temperature dependence on height is an important parameter that may prevent the system from accomplishing thermal balance at certain spatial locations. The implications of these results are discussed in detail., Comment: Accepted for publication in A&A

We propose and unify classes of different models for information propagation over graphs. In a first class, propagation is modelled as a wave which emanates from a set of \emph{known} nodes at an initial time, to all other \emph{unknown} nodes at later times with an ordering determined by the arrival time of the information wave front. A second class of models is based on the notion of a travel time along paths between nodes. The time of information propagation from an initial \emph{known} set of nodes to a node is defined as the minimum of a generalised travel time over subsets of all admissible paths. A final class is given by imposing a local equation of an eikonal form at each \emph{unknown} node, with boundary conditions at the \emph{known} nodes. The solution value of the local equation at a node is coupled to those of neighbouring nodes with lower values. We provide precise formulations of the model classes and prove equivalences between them. Finally we apply the front propagation models on graphs to semi-supervised learning via label propagation and information propagation on trust networks.

Data required to calibrate uncertain GCM parameterizations are often only available in limited regions or time periods, for example, observational data from field campaigns, or data generated in local high-resolution simulations. This raises the question of where and when to acquire additional data to be maximally informative about parameterizations in a GCM. Here we construct a new ensemble-based parallel algorithm to automatically target data acquisition to regions and times that maximize the uncertainty reduction, or information gain, about GCM parameters. The algorithm uses a Bayesian framework that exploits a quantified distribution of GCM parameters as a measure of uncertainty. This distribution is informed by time-averaged climate statistics restricted to local regions and times. The algorithm is embedded in the recently developed calibrate-emulate-sample (CES) framework, which performs efficient model calibration and uncertainty quantification with only $\mathcal{O}(10^2)$ model evaluations, compared with $\mathcal{O}(10^5)$ evaluations typically needed for traditional approaches to Bayesian calibration. We demonstrate the algorithm with an idealized GCM, with which we generate surrogates of local data. In this perfect-model setting, we calibrate parameters and quantify uncertainties in a quasi-equilibrium convection scheme in the GCM. We consider targeted data that are (i) localized in space for statistically stationary simulations, and (ii) localized in space and time for seasonally varying simulations. In these proof-of-concept applications, the calculated information gain reflects the reduction in parametric uncertainty obtained from Bayesian inference when harnessing a targeted sample of data. The largest information gain typically, but not always, results from regions near the intertropical convergence zone (ITCZ).

Testing, contact tracing, and isolation (TTI) is an epidemic management and control approach that is difficult to implement at scale because it relies on manual tracing of contacts. Exposure notification apps have been developed to digitally scale up TTI by harnessing contact data obtained from mobile devices; however, exposure notification apps provide users only with limited binary information when they have been directly exposed to a known infection source. Here we demonstrate a scalable improvement to TTI and exposure notification apps that uses data assimilation (DA) on a contact network. Network DA exploits diverse sources of health data together with the proximity data from mobile devices that exposure notification apps rely upon. It provides users with continuously assessed individual risks of exposure and infection, which can form the basis for targeting individual contact interventions. Simulations of the early COVID-19 epidemic in New York City prove the concepts. In the simulations, network DA identifies up to a factor 2 more infections than contact tracing when both harness the same contact data and diagnostic test data. This remains true even when only a relatively small fraction of the population uses network DA. When a sufficiently large fraction of the population ($\gtrsim 75\%$) uses network DA and complies with individual contact interventions, targeting contact interventions with network DA reduces deaths by up to a factor 4 relative to TTI. Network DA can be implemented by expanding the computational backend of existing exposure notification apps, thus greatly enhancing their capabilities. Implemented at scale, it has the potential to precisely and effectively control future epidemics while minimizing economic disruption.