## Abstract

Odour plumes in the wild are spatially complex and rapidly fluctuating structures carried by turbulent airflows^{1,2,3,4}. To successfully navigate plumes in search of food and mates, insects must extract and integrate multiple features of the odour signal, including odour identity^{5}, intensity^{6} and timing^{6,7,8,9,10,11,12}. Effective navigation requires balancing these multiple streams of olfactory information and integrating them with other sensory inputs, including mechanosensory and visual cues^{9,12,13}. Studies dating back a century have indicated that, of these many sensory inputs, the wind provides the main directional cue in turbulent plumes, leading to the longstanding model of insect odour navigation as odour-elicited upwind motion^{6,8,9,10,11,12,14,15}. Here we show that *Drosophila* *melanogaster* shape their navigational decisions using an additional directional cue—the direction of motion of odours—which they detect using temporal correlations in the odour signal between their two antennae. Using a high-resolution virtual-reality paradigm to deliver spatiotemporally complex fictive odours to freely walking flies, we demonstrate that such odour-direction sensing involves algorithms analogous to those in visual-direction sensing^{16}. Combining simulations, theory and experiments, we show that odour motion contains valuable directional information that is absent from the airflow alone, and that both *Drosophila* and virtual agents are aided by that information in navigating naturalistic plumes. The generality of our findings suggests that odour-direction sensing may exist throughout the animal kingdom and could improve olfactory robot navigation in uncertain environments.

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## Data availability

All experimental data are available at Dryad (https://doi.org/10.5061/dryad.1ns1rn8xd). Source data are provided with this paper.

## Code availability

All data collection was performed using custom codes written in Python (v.3.65), using the scientific packages numpy and scipy, plotting package matplotlib and the stimulus generation package psychopy. Custom Python codes used for projecting fictive odour stimuli, for fly tracking, and for behavioural and signal extraction and smoothing are available at GitHub (https://github.com/emonetlab/opto-track).

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## Acknowledgements

We thank O. Mano for help with projector troubleshooting, and A. Sehdev, E. Brown and G. Santana for help with behavioural experiments, fly rearing and discussions; V. Jayaram, J. Carlson, J. Jeanne, and the members of the Emonet laboratory for discussions and advice on the project; members of the laboratories of M. Murthy and J. Carlson for fly strains. N.K. was supported by a postdoctoral fellowship through the Swartz Foundation for Theoretical Neuroscience, by postdoctoral fellowships NIH F32MH118700 and NIH K99DC019397. M.D. was partially supported by the Program in Physics, Engineering and Biology at Yale University. B.T.M. and M.A.R. were supported by National Science Foundation grant IIS-1631864. B.D.D. was supported by an NSF GRF. D.A.C. and this research were supported by NIH R01EY026555. T.E. and this research were supported by T.E.’s setup funds from Yale University. Portions of this research were conceived at the Kavli Institute for Theoretical Physics summer school (NSF PHY-1748958).

## Author information

### Authors and Affiliations

### Contributions

N.K., D.A.C. and T.E. designed the research. B.D.D. conceived the projector-based virtual set-up. N.K. and M.D. built the assay with inputs from D.A.C. and T.E.; N.K. performed all experiments, data analysis and agent-based simulations. M.D. performed the electrophysiology. B.T.M. and M.A.R. performed the numerical simulations for Fig. 5. N.K. and T.E. performed the theoretical analysis of the turbulent plume. N.K., D.A.C. and T.E. validated the data. N.K., D.A.C. and T.E. discussed the data analysis. N.K. wrote the initial draft, and N.K., D.A.C. and T.E. contributed to all revisions. All of the authors approved the final manuscript.

### Corresponding authors

## Ethics declarations

### Competing interests

The authors declare no competing interests.

## Peer review

### Peer review information

*Nature* thanks Bing Brunton and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

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## Extended data figures and tables

### Extended Data Fig. 1 Verification of odour velocity calculation and distributions of signal-derived quantities in measured plume.

**a**, Mean odour velocity measured in the virtual antenna at all times for navigating flies in measured smoke plume, plotted as a function of fly orientation. The -\({\rm{\cos }}\left(\theta \right)\) trend reflects the fact that the main component of odour velocity is parallel to the mean wind direction \(9{0}^{o}\), as expected – a consistency check on the odour velocity calculation. **b–d**, Histograms of signal-derived quantities measured in the fly virtual antenna; the *x*-axis limits in Fig. 1c–e are determined by the extent of these histograms.

### Extended Data Fig. 2 Electrophysiological and behavioural verification of optogenetic activation of *Drosophila* ORNs.

**a**, Extracellular measurements of ab2A firing rates for various odour signals mimicking those we use throughout our study. Stimuli (red shades) are delivered using a Luxeon Rebel 627 nm red LED (Lumileds Holding B.V., Amsterdam, Netherlands) at 10 uW/mm^{2}. The frequency and duty cycle for the stimuli in the first plot are 1.5 Hz and 50% respectively, which mimics what a stationary fly in the 5 cm wide, 15 mm s^{−1} fast moving bars (Fig. 2b) would encounter. Longer stimuli approximate the stimuli experienced in the wide moving bars (Fig. 2e, f). The bottom plot shows the firing rate in response to the stimulus experienced by one representative measured fly navigating 15 mm s^{−1} moving wide bars. All recordings were taken from 5 ab2a ORNs in 2 different flies. **b**, Illustrative track of a fly following stationary fictive odour ribbons upwind. Red bars: optogenetic stimulus location – bars are overlaid on the figure, but not actually imaged since the image is IR-pass filtered. **c**, Fictive odour signal experienced by a fly (red bars) can be quantified simultaneously with fly behaviour (teal) by aligning the camera and projector coordinate systems (Methods). Plotted are the fictive odour signal and behaviour for the track shown in **b. d**, Verification that flies on both the top and bottom glass surfaces of the assay respond similarly to the fictive odour signals (here, 3 odour ribbons in laminar wind; scale bar: 2 cm; left). Flies were manually annotated as being on the top or bottom surface. In both cases (middle and right; scale bar: 2 cm), flies followed the fictive odour ribbons upwind, similar to behavioural responses with real odours^{10}.

### Extended Data Fig. 3 Odour direction selectivity in single antenna and single Or flies, and ON/OFF edge responses across speeds and for negative controls.

**a**, Component of fly walking velocity along +*x* direction during the 5s stimulus (shaded grey) and blank periods (illustrated in Fig. 2b), in *Orco*>Chrimson flies that have one antenna ablated (compare to Fig. 2c). Shaded errors: SEM. Blue and orange denote rightward and leftward moving bars, respectively. Since it is difficult to distinguish flies walking on the top and bottom surface of the assay, right- and left-antenna ablated flies are pooled. *n* = 100, 89 tracks for rightward and leftward bar motion, respectively. Only flies oriented in the 90^{o} sector perpendicular to the bar motion are included. **b**, Distribution of fly orientations during the 5s stimulus (top) and 5s blank periods (bottom), for rightward (blue) and leftward (orange) bar motion, *Orco*>Chrimson flies with one antenna ablated (compare Fig. 2d). Orientations are symmetrized over the *x*-axis. **c-d**, Same as **a**-**b**, for *Or42b*>Chrimson flies with both antennae intact. *n* = 37, 50 tracks for rightward and leftward bar motion, respectively. **e**, Turning bias for all instances in which flies encounter the fictive odour ON (green) or OFF (purple) edge, for flies oriented within a \({90}^{o}\) sector of the direction perpendicular to bar motion. Turning bias is calculated as the sign of fly orientation change from 150 ms to 300 ms after the edge hit. All flies are *Orco*>Chrimson and fed ATR (i.e. optogenetically active) except in the 7^{th} plot, which are not fed ATR. Data are shown for bars that move at various speeds (left 6 plots), as well as for negative controls (7^{th} and 8^{th} plot). Error bars: SEM. *P* values calculated using the chi-squared test (*****p* < 10^{−4}, ****p* < 10^{−3}, ***p* < 10^{−2}, **p* < 0.05). Specifically, *p* = 9.60×10^{−5} for *n* = 1472 ON edge hits and *p* = 0.23 for *n* = 1661 OFF edge hits for 30 mm s^{−1} bars; *p* = 3.49×10^{−3} for *n* = 1167 ON edge hits and p = 0.132 for *n* = 1306 OFF edge hits for 20 mm s^{−1}; *p* = 1.03×10^{−6} for *n* = 548 ON edge hits and *p* = 1.18×10^{−3} for *n* = 470 OFF edge hits for 15 mm s^{−1}; *p*<10^{−6} for *n* = 1125 ON edge hits and *p* = 1.78×10^{−5} for *n* = 1039 OFF edge hits for 10 mm s^{−1}; *p* < 10^{−6} for *n* = 1000 ON edge hits and p = 0.816 for *N*=987 OFF edge hits for 5 mm s^{−1}; *p* = 0.012 for *n* = 1284 ON edge hits and p = 0.2106 for *n* = 1633 edge hits for 1 mm s^{−1}; *p* = 0.423 for *n* = 1387 ON edge hits and *p* = 0.701 for *n* = 1484 OFF edge hits for no ATR 10-15 mm s^{−1}; and *p* = 0.0295 for *n* = 988 ON edge hits and *p* = 0.454 for *n* = 1153 OFF edge hits for 1 antenna 10-15 mm s^{−1}. Direction selectivity is satisfied if both ON and OFF edge responses have the same sign; gradient sensing would require opposite signs for the two edges. Data indicate that flies counterturn against the direction of fictive odour bars at both edges, within a range of bar speeds. Large ON responses for slow bar speeds are likely attributed to gradient sensing: since the direction of odour motion and gradients are the same for ON edges but opposite for OFF edges, this would give appreciable ON edge responses at slower speeds, but diminished OFF edge responses. **f**, Turning responses for Or42b > Chrimson flies, in which light activates only one ORN type, in response to bars moving at 10-15 mm s^{−1}. Error shades: SEM. Turning responses are consistent with direction selectivity (compare with Fig. 2f). *p* = 4.82×10^{−3} for *n* = 706 ON edge hits and *p* = 5.51×10^{−3} for *n* = 763 OFF edge hits. **g**, Dependence of the results on the choice of the window over which the turning bias is calculated. The *x*-axis shows the onset time of the window; the offset time was 150 ms later. The *y*-axis plots the turning bias for flies oriented within a 90^{o} sector of the direction perpendicular to bar motion (as in **e**). “Experimental” flies refer to *Orco* > Chrimson in response to bars moving at 10–15 mm s^{−1} (same as in Fig. 2); “no-ATR” and “1 antenna” are the same flies not fed ATR or with only 1 antenna, respectively. The “null” condition is calculated using random chosen trajectories and calculating angle changes following fictitious moving bars at random angles not actually presented to the flies. Over window onsets of 0-200 ms, the *no ATR*, *1 antenna* and *null* responses are all within the same regime (< ~0.1), while the experimental responses are significantly higher. These results are consistent with previous findings. OFF response reaction times of ~500 ms have been observed^{9}, but those were for flies counterturning back into static ribbons – the differing locomotive repertoire (flying vs. walking) and plume dynamics (static vs. dynamic) would account for this discrepancy. Reaction times of 400 ms have been observed for walking flies, but this may reflect imprecision in odour delivery^{6}; indeed, reaction times are as low as 100 ms for tethered flies whose ORNs are stimulated optogenetically^{17} and as low as 85ms when ORNs are stimulated with real odours^{25}.

### Extended Data Fig. 4 OFF edge responses in laminar wind and ON edge responses for fast 30 mm s^{−1} bars.

**a**, Turning bias versus fly orientation when bilateral optogenetic stimulus is turned off (compare with the first plot in Fig. 3b for flash onset). *n* = 1490 OFF flash hits. **b–d**, Fly turning bias for 15 mm s^{−1} bars moving parallel, antiparallel, and perpendicular to 150 mm s^{−1} laminar wind (compare with Figs. 3de). Shaded errors: SEM. *n* = 1493, 1588, and 671 OFF edge encounters for bars parallel, antiparallel, and perpendicular to the wind, respectively. **e**, Fly turning bias vs. fly orientation at ON edge for faster 30 mm s^{−1} fictive odour bars without wind (analogous to 15 mm s^{−1} bar responses in second plot of Fig. 3c). Dotted line: fit of response to \(-0.16{\rm{\cos }}\theta \). *N* = 1472 ON edge encounters. **f**, Additive model for ON edges of 30 mm s^{−1} bars; analogous to Figs. 3de. Solid shaded region: mean \(\pm \) 1 SEM; dotted lines: additive model prediction. *N* = 323, 319, and 1013 ON edge encounters for odour bars with parallel, antiparallel, and perpendicular to the wind, respectively.

### Extended Data Fig. 5 Supplementary figures and additional evidence that direction sensing is enacted using a correlation-based algorithm.

**a**, Schematic illustrating calculation of latency \(\Delta T\) between antennae hits for moving edges. Correlation-based models for direction selectivity depend on the latency \(\Delta T\) of the time at which the edge hits the two sensors – in this case, the fly’s two antennae. Measuring \(\Delta T\) does not require resolving the image or stimulus at antennal resolution (~300 \(\mu \)m), rather \(\Delta T\) can be inferred with knowledge of the fly’s orientation relative to the bar direction \(\varphi \), as well as the speeds of the fly and bar – all of which are known. See Methods for details of the calculation and an estimate of the uncertainty. **b**, Spatiotemporal correlation functions for correlated noise stimuli (Fig. 4c–f). Each type of correlated noise stimulus is characterized by the correlation function \(C(\Delta x,\Delta t)\) computed between all pairs of bars separated spatiotemporally by \(\Delta x\) pixels and \(\Delta t\) frames. Since our stimuli are generated by summing and binarizing Gaussian variables, nonzero correlations off of the origin have magnitude 1/3^{26}. For example, for positively correlated with-wind stimuli (top left plot), \(C\left(1,1\right)=C\left(-1,-1\right)=1/3\), and the remaining correlations are zero, while for negatively correlated with-wind stimuli (bottom left plot), \(C\left(1,1\right)=C\left(-1,-1\right)=-1/3\). **c**, Snapshots of *glider* stimulus with correlations along \(+x\) axis, for 3 consecutive frames. In one instance of time, the stimulus is a random pattern of light and dark 1-pixel-wide bars perpendicular to the 150 mm s^{−1} laminar wind. Each \(x\)-pixel is perfectly correlated with the pixel to its right in the next frame; thus the pattern in the next frame is the same as the pattern in the current frame, but shifted by one pixel. Visually, this would be perceived as a fixed pattern moving coherently to the right in discrete steps. **d**, Like correlated noise stimuli, gliders are defined by their correlation matrix \(C(\Delta x,\Delta t)\). Unlike correlated noise, the correlations i) have magnitude 1, and ii) exist for many spacetime points. That is, for rightward correlated gliders, a given pixel in a given frame is perfectly correlated with the pixel to its right one frame later, but also with the second pixel to its right 2 frames later, etc. Thus \(C(\Delta x,\Delta t)\) has values +1 along the diagonal. Similarly, \(C(\hspace{-.25mm}-\hspace{-.25mm}\Delta x,\Delta t)\) has values 1 along the anti-diagonal. Since \(+x\) points downwind, we call gliders with correlations to the right “with-wind”, and gliders with correlations to the left “against-wind,” in analogy to the correlated noise stimuli (Fig. 4d). **e**, Turning bias versus fly orientation for with-wind (blue) and against-wind (red) gliders. Data using pattern update rates of 45 or 60 Hz are pooled. Shaded errors: SEM. Gliders are presented in 4s blocks, interleaved with 4s of no stimulus. Turning bias is defined as the sign of the change in orientation from 200 to 500 ms after the block onset. We only used flies with speeds < 12 mm s^{−1} for gliders, since long-range correlations can interfere with the intended correlation if fly walking speed is near the glider speed. *n* = 301, 247 onset events, for with-wind and against-wind, respectively. **f**, Turning bias averaged over all orientations for different glider speeds. Glider speed is calculated as (pixel width)\(\times \)(pattern update rate) where the pixel width is 290 µm and the pattern rate is some multiple of the inverse frame rate, 1/(180 Hz). *n* = 141, 163, 138, 190 onset events for with-wind stimuli at glider speeds 25, 16, 12, and 10 mm s^{−1}, respectively; *n* = 159, 119, 128, 137 onset events for against-wind stimuli at same glider speeds, respectively. **g**, For correlated stimuli to be sensed in our assay, the bar width (size of \(x\)-pixel, 290 µm), must be on the order of the fly antennal separation (\(\sim \)300 µm^{58}). **h**, Glider stimuli experiments repeated for bars that were double the width, 580 µm. Differences now disappear for with and against-wind correlations, consistent with bilaterally enabled direction sensing, since these bars are too wide to consistently stimulate antennae differentially. Shaded errors: SEM. *n* = 195, 169 onset events for with-wind and against-wind, respectively.

### Extended Data Fig. 6 HRC response is robust to signal pre-filtering.

Minimum resolvable inter-antennal latency \(\Delta T\) as a function of the noise level, for exponential pre-filters of varying timescale, \({\tau }_{{\rm{smear}}}=1,15,50\) ms, respectively, for the 3 plots. Noise level is quantified as a random shift of \(\Delta T\), where each shift is chosen from a normal distribution with mean zero and standard deviation \(\delta t\). The HRC’s delayed arm has an exponential filter of timescale \({\tau }_{{\rm{HRC}}}\) = 15 ms. Dotted line: identity. A particular value of \(\Delta T\) is deemed resolvable if the SD over HRC responses is greater than the mean over HRC responses (see Methods for details). The mean and SD are calculated over 100 samples (i.e. 100 random shifts of \(\Delta T)\) for a given noise level \(\delta {\rm{t}}\).

### Extended Data Fig. 7 Odour velocity and concentration gradients provide complementary directional information in complex plumes.

**a**, Vector field of the negative gradient of odour concentration \(-\nabla c\), averaged over the full simulation (compare to Fig. 6c in the main text). Gradients contain strong lateral components near the odour source. **b**, Time course of an estimate of the direction of odour motion \({\theta }_{{\rm{odor}}}={\tan }^{-1}({{\bf{v}}}_{y,{\rm{odor}}},{{\bf{v}}}_{x,{\rm{odor}}})\) at the centre of the boxed regions in Fig. 6a, determined by averaging all detectable \(\theta \) in the past *t* seconds. Error bars are found by repeating this for 16 different 10 s time windows throughout the simulation, and taking the average and standard deviation over these 16 samples – these correspond to the mean and standard error of the mean. Dots indicate the time needed to distinguish the direction of odour motion from \({0}^{\text{o}}\) (downwind) with a 68% confidence level for the 3 regions. **c**, Heatmap of time taken to distinguish the direction of odour motion from \({0}^{\text{o}}\) to within 68% confidence for fixed locations throughout plume. Black values include the possibility that the odour motion direction is not distinguishable from downwind no matter how long one samples.

### Extended Data Fig. 8 Odour motion sensing aids plume navigation by increasing lateral motion toward the plume centerline.

**a**, Average change in position parallel to wind, *x* (left), and away from the plume centerline, |*y*| (right), in outward (purple) and inward (green) moving bars plume (Fig. 6d), as a function of time. Note that *x* = 0, *y* = 0 is the fictive plume’s odour source location. The initial values at \(t=0\) of *x* (*y*) were subtracted, so the change \(\Delta x\) (\(\Delta y\)) is plotted – this is negative because flies progress toward to the centerline (decreasing *y*) and upwind (decreasing *x*). Only flies beginning in the rear 50 mm of the arena and which navigated for at least 30s were considered. Shades: SEM over distinct fly trajectories. Dotted lines: times *t* = 10, 20, 30s. By *t* = 20s, flies in the outward bar plume have made more progress both in the upwind direction (*p* = 0.025; 1-tailed *t*-test) and toward the plume centerline (*p* = 0.032; 1-tailed *t*-test). **b**, same for fictive odour plume shown in Fig. 6g, played normally (purple) or in reverse (green). Here, flies make equal progress upwind by 30s (left plot), but significantly faster progress toward the plume centerline in the forward played plume than the reverse one (right plot) (*p* = 0.035 at *t* = 10s, *p* = 3.0×10^{–3} at *t* = 20s, at *p* = 1.6×10^{–4} at *t* = 30s; 1-tailed *t*-test). Shades: SEM over distinct fly trajectories.

### Extended Data Fig. 9 Odour motion sensing enhances performance of virtual robots obeying a simple navigation strategy on a grid.

**a**, Model of 2-sensor virtual agents navigating the simulated odour plume (Fig. 6a). Agents are always oriented at 0^{o}, 90^{o}, 180^{o} or 270^{o}, and at each timestep turn 90^{o} either left or right and move forward one step. Agents are either odour direction sensing (DS+) or not odour direction sensing (DS-). When odour concentration \(c\) exceeds some threshold \({c}_{0}\), DS- agents turn upwind. DS+ agents, for \(c > {c}_{0}\), turn against the direction of odour motion when oriented upwind or downwind; crosswind agents always turn upwind. DS+ agents infer the direction of odour signals using an HRC-like computation between their 2 sensors (Methods). **b**, Example trajectories of robots navigating plume in **a**, when they are initialized in the back 50 mm of the arena, for DS- (top) and DS+ (bottom) agents. **c**, Percentage of 500 agents reaching the 50x50 mm red source region; more DS+ agents reach the source than DS- agents (38% vs. 19%; *p* < 10^{–6}; 1-tailed *t*-test) **d**, Lateral distance from plume axis \({|y|}\) over time, for agents initialized near the plume edges (>60 mm from plume axis, indicated by the solid boxes in **b**; top plot) or near the plume axis (<60 mm from axis, indicated by the dashed boxes in **b**; bottom plot). Odour direction sensing enhances lateral drift toward the plume centerline, particularly for robots initialized at the plume edges.

### Extended Data Fig. 10 Odour velocity in model of turbulent plumes points outward from plume centerline and is computed by local space-time correlators.

We use a simple packet model of turbulent plumes. Packets are released from a source and disperse in the lateral direction while being advected downwind (see Methods for model and calculation details). **a**, Packet velocity \({\langle v\rangle }_{y,t}\) in the plume model, as a function of \(\bar{y}=y/\sqrt{T}\), for two correlation times, \(T=0.2\) (purple) and \(T=1\) (green), at a fixed time \(t=4\). Here, \(v\) is set to 1. To directly compare velocity for plumes with different *T*, (and therefore different diffusivities) we plot the velocity versus the normalized length \(\bar{y}\). Specifically, since \(\left\langle {y}^{2}\right\rangle =2T{v}^{2}t\) for \(t\gg T\) then at a given \(t\), the packet distribution in terms of \(\bar{y}\) is the same for plumes with distinct \(T\). The distribution of packets for either \(T\) is a function of \(\bar{y}\) shown in grey. The velocity is an odd function of \(y\), i.e. it points outward from the plume axis. In addition, the asymmetry is steeper for higher correlation times. **b**, The value of the correlator \(\left\langle {\rm{C}}\left(\Delta y,\Delta t|y,t\right)\right\rangle \)as a function of lateral distance \(y\), for various times \(t\) for \(T=0.1\) (left) and \(T=0.3\) (right). Here, \({D}_{p}=0.005\). Since the packets are advected downwind with a velocity \(U\gg v\), the time axis is proportional to the downwind distance. The packet distribution is shown on the bottom; the limits of the \(y\)-axis are chosen such that the plume extents are the same in both plots. **c**, The total *y-*integral of the absolute value of \(\left\langle {\rm{C}}\left(\Delta y,\Delta t|y,t\right)\right\rangle \) at a fixed \(t=4\), as a function of odour packet speed (\(y\)-axis) and molecular diffusivity (\({D}_{p}\)), with \(T=1\), \(v=1\). This integral indicates the degree of directional sensing on average. The integral is highest for greater packet speeds and lower molecular diffusivities (top left corner).

## Supplementary information

### Supplementary Discussion

Additional discussion of (1) the HRC model in odour motion sensing and its comparison to visual motion sensing and (2) the role of antennal size, active sensing and flight in odour motion sensing.

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Kadakia, N., Demir, M., Michaelis, B.T. *et al.* Odour motion sensing enhances navigation of complex plumes.
*Nature* **611**, 754–761 (2022). https://doi.org/10.1038/s41586-022-05423-4

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DOI: https://doi.org/10.1038/s41586-022-05423-4

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