Many species rely on olfaction to navigate towards food sources or mates. Olfactory navigation is a challenging task since odor environments are typically turbulent. While time-averaged odor concentration varies smoothly with the distance to the source, instaneous concentrations are intermittent and obtaining stable averages takes longer than the typical intervals between animals’ navigation decisions. How to effectively sample from the odor distribution to determine sampling location is the focus in this article. To investigate which sampling strategies are most informative about the location of an odor source, we recorded three naturalistic stimuli with planar lased-induced fluorescence and used an information-theoretic approach to quantify the information that different sampling strategies provide about sampling location. Specifically, we compared multiple sampling strategies based on a fixed number of coding bits for encoding the olfactory stimulus. When the coding bits were all allocated to representing odor concentration at a single sensor, information rapidly saturated. Using the same number of coding bits in two sensors provides more information, as does coding multiple samples at different times. When accumulating multiple samples at a fixed location, the temporal sequence does not yield a large amount of information and can be averaged with minimal loss. Furthermore, we show that histogram-equalization is not the most efficient way to use coding bits when using the olfactory sample to determine location.
Diverse species throughout the animal kingdom use olfactory cues for navigation tasks critical to survival, including locating food sources and mating partners. However, olfactory navigation is not simple: odorants are often volatile and carried on rapidly changing currents, resulting in spatiotemporal distributions that are turbulent thereby defeating simple strategies such as gradient detection. Consequently, recent efforts at understanding olfactory navigation have focused on identifying the viable computational strategies for making navigation decisions [1,2]. Here we focus on the most basic aspect of this process: how odor samples are encoded in the first place. Since sensory resources are finite, tradeoffs are inevitable. For example, resources may be allocated to encoding individual samples of odor concentration at a fine level of detail, or alternatively, to encoding multiple samples, either in space or in time, but at a coarser resolution for concentration. In this study, we investigate the implications of these and related tradeoffs, using the tools of information theory. Specifically, we compare an array of sampling and encoding strategies, asking to what extent they capture information about location within an olfactory environment. There are several aspects of the statistics of an odor plume that can give clues as to the location of the source [3–7]. For example, the mean concentration varies smoothly in lateral and longitudinal directions. However, animals do not base their navigation decisions on mean concentration, as the time it takes to obtain stable estimates of mean concentration exceeds the typical time taken by animals to make navigation decisions [8–10]. Other olfactory features that have been proposed as useful for navigation decisions include the time between odor encounters [11–13] and intermittency (the probability of the odor concentration above threshold) [4]. However, as for mean concentration, obtaining stable estimates of these quantities takes more time than animals typically use for navigation decisions. Hence averaged quantities—even if aided by other sensory inputs—are probably not used to guide navigation decisions. These considerations motivate our focus on what can be learned from brief, localized samples. We do not address the issue of how to integrate odor samples with other sources of information. A key starting point for our analysis is the explicit recognition that the resources available for sampling and encoding an odor environment are finite, and that it is natural to quantify these resources in terms of bits. This leads to the framework of information theory, which has the advantage that it minimizes the assumptions about the odor distribution. As mentioned above, the sampling strategies we consider explore tradeoffs between the number of bits allocated to resolving concentration, and to sampling in space and time. The focus on these tradeoffs is motivated by the diversity of the sampling strategies that animals use. With regard to spatial aspects, most animals have two spatially separated antennae or nostrils which sample the olfactory environment, but the sensor spacing ranges from less than a mm to several cm. With regard to temporal aspects, insects’ olfactory receptors are continuously exposed to odorants, while rodents take periodic samples and adjust their sniff rate based on previous measurements [14–16]. In this article, we discuss sampling strategies based on local cues in light of how much information they provide about sampling location. To compare different sampling strategies, we computed the information that they conveyed about location, for three realistic olfactory environments. In each environment, odor concentration was empirically determined via physical measurements, planar laser-induced fluorescence [17]. We chose to use physical measurements of actual plumes not only to avoid the assumptions made by models of turbulence or the complexities of numerical simulations, but also because the non-idealities of physical measurements take into account the real-world issues that confront the olfactory navigator. Although the three environments differed with regard to flow rate, turbulence, and proximity to a boundary, a number of commonalities emerged. First, precise measurement of odor concentration is generally not useful. That is, after allocating one or two bits to a coarse representation of odor concentration, more information about location is gained by using additional bits for encoding concentrations at nearby locations in space or time, than by using these bits to refine the representation of concentration. We also demonstrate that using “histogram equalization” as a strategy to discretize odor concentration—which is optimal to convey information about intensity per se [18]—is not optimal when the goal is to determine location. That is, the optimal strategy for low-level sensory encoding depends on the ultimate use of the information. Finally, with regard to sampling in time, we find that the additional information gained from multiple samples is preserved even if the temporal order of the samples is ignored, and this provides a rationale for simple post-receptoral processing strategies.
Odor plume data were obtained experimentally using a surrogate odor (acetone) released in a turbulent flow within a benchtop low-speed wind tunnel. We imaged the odor structure using planar laser-induced fluorescence (PLIF); images were subsequently post-processed into calibrated matrices of normalized concentrations. We acquired three separate datasets varying in mean flow rates and proximity to a boundary. The wind tunnel has a test section measuring 1 m long, by 0. 3 m tall, by 0. 3 m wide. We collected odor plume data at flow speeds of 5 cm/s and 10 cm/s. Ambient air enters the tunnel through a contraction section and passes through a turbulence grid consisting of 6. 4 mm diameter rods with a 25. 5 mm mesh spacing. Air exits the test section through a 15 cm long honeycomb section used to isolate the test section from a fan located in the downstream contraction. The odor surrogate was released isokinetically through a 9. 5 mm diameter tube on the tunnel centerline. The tube orifice was located 10 cm downstream of the turbulence grid. For one dataset, named boundary flow, a false floor spanning the length and width of the test section was placed directly below the release tube. Acetone vapor was used as a fluorescent odor surrogate. We generated the acetone vapor by bubbling a carrier gas through liquid acetone. Because acetone is denser than air, the carrier gas consisted of a mixture of air (59% v/v) and helium (41% v/v) such that the odor surrogate mixture was neutrally buoyant in the wind tunnel. We used a water bath to maintain the temperature of the odor mixture at ambient tunnel conditions. A 1 mm thick light sheet from a Nd: YAG 266 nm pulsed laser illuminated the odor plume in the test section, causing acetone vapor in the odorant mixture to fluoresce with an intensity proportional to its concentration. The laser sheet enters and exits the tunnel through longitudinal slits along the sides of the test section. Plume fluorescence was imaged through a glass window in the tunnel using a high quantum efficiency sCMOS camera, with a bit depth of 16 bit, at a framerate of 15 Hz synchronized with the laser pulses. To enhance signal-to-noise, images were binned to (512x512) pixels corresponding to a spatial resolution of 0. 74 mm/pixel. Raw images were processed to correct for background according to the equation c (t, x, y) =1acI (t, x, y) F (x, y), (1) where c is the normalized concentration, I is the image from the camera (with background signal subtracted) and F is the flatfield image (also with the background signal subtracted). The calibration coefficient, ac, was used to normalize the concentrations based on the source concentration at the tube exit. Three datasets were collected, which had different combinations of wind tunnel flow rates and false floor configurations (Table 1). The first condition, named fast flow, had a mean free stream velocity of 10 cm/s, and the odor mixture was released into the center of the tunnel without a false floor. The second condition, named slow flow, had a free stream velocity of 5 cm/s, and acetone was also released into the center of the tunnel without a false floor. The third condition (boundary flow) had a free stream velocity of 10 cm/s, but in contrast to the first condition, acetone was released with the false floor in place. All datasets were collected in segments of 4 minutes. We had a total of 40 minutes (36000 frames) for the first and third condition, and 36 minutes (32400 frames) for the second dataset. The matrices of normalized concentrations provide a natural coordinate system. Time-averaged odor concentrations and two typical snapshots for the three conditions are shown in Fig 1. To compare olfactory cues across different flow conditions, we chose two grids of 16 locations in each olfactory landscape (G narrow and G wide). Coordinates of the locations for the grid choices (inlet location at the origin) are: G narrow = { (x, y) | x = (2. 2,5. 9,9. 6,13. 3) cm, y = (- 4. 4, - 1. 5,1. 5,4. 4) cm }, G wide = { (x, y) | x = (5. 6,11. 1,16. 7,22. 2) cm, y = (- 2. 6, - 1. 1,1. 1,2. 6) cm }. (2) The two grids were chosen to capture the environment close to the source and further away from it above and below the centerline. The locations are indicated as blue circles (G narrow) and green triangles (G wide) in Fig 1. The distances between gridpoints and the odor source are directly relevant to walking flies and other small insects. Probability distributions of the odor concentrations of the upper half of all grid points are shown in S1 Fig. Our primary goal is to quantify the extent to which a small number of samples of odor concentration within a plume provide information about the location of the sample. A principled approach is to use Shannon’s mutual information (MI) [19] for this purpose. That is, using entropy as a measure of uncertainty, we will determine the extent to which a given encoding scheme reduces the uncertainty about the location of the sample. Thus, our two variables of interest are location (L) and discretized odor samples (M); these are related in a complex statistical fashion. Specifically, this analysis quantifies the ability to discriminate between the 16 locations of either G narrow or G wide when the only available information comes from odor intensity samples. The choice of 16 locations per grid is somewhat arbitrary, however, in order to get stable information estimates with a given amount of data one trades off the number of locations with the number of bits using for odor coding. We settled on 16 locations as they capture a good proportion of the environment while allowing for the analysis of coding of odor samples with up to 10 bits. As is well-known, the MI between two random variables L and M is [19,20]: I (L, M) = H (L) - ∑ m ∈ M p (m) H (L | m), (3) where H (L) is the (unconditional) entropy of L, and H (L | m) is the entropy of the distribution of L conditional on m ∈ M. In our context, L is the set of sampling locations G narrow or G wide and m ∈ M is a measurement of the normalized odor concentration c (t, x, y). The specific representation of c as a (coarser) measurement m is an integral part of the encoding schemes we consider. We assume that the a priori probability of the locations l ∈ L are equal. It follows that the unconditional entropy is H (L) = - ∑ l ∈ L p (l) log 2p (l) = log (| L |), (4) where | L | is the number of sampling locations. Note that the MI (Eq 3) is a property of the grid as a whole, not the individual points. Since all | L | grid points have the same a priori probability, the upper bound of the MI is log 2 (| L |). If the navigator has log 2 (| L |) bits of information then it knows its location on the grid unambigously. Posterior (conditional) distributions p (l|m) were calculated by Bayes theorem. Specifically, we binned the odor concentrations c at each location p (m|l) and then normalized the likelihoods by p (m). The entropy of these conditional distributions are given by H (L | m) = - ∑ l ∈ L p (l | m) log 2 p (l | m). (5) This quantity, weighted by the probability that sample m occurs p (m), is summed over all m ∈ M to determine the average conditional entropy in Eq (3). We used two contrasting strategies for representing the odor concentration as discrete symbols (bins). In the first strategy, we divided the data into equal quantiles, i. e. we chose boundaries such that the distribution p (m) is uniform. This histogram-equalization procedure maximizes the information conveyed about the odor concentration (i. e. , M) [20, chap. 2], but does not necessarily maximize the information conveyed about sampling location. In the second strategy, we adjusted these bin boundaries to increase the amount of information about location. Because finding the bin boundaries that yield an absolute maximum is a multidimensional discrete optimization problem, we used the following “greedy” iterative strategy to find an approximate maximum. The first bin boundary is chosen to maximize I (L, M), and is identified by an exhaustive search of the range of concentrations. Then, iteratively, the k-th boundary is chosen to maximize I (L, M) while keeping the k − 1 bin boundaries fixed. This is also a one-dimensional search over the range of concentrations, and leads to a binary subdivision of one of the bins determined at the previous step. For analyses in which the odor at multiple temporal or spatial samples is encoded, we used the bin boundaries determined from these single-sample optimizations. The encoding strategies we considered are specified not only by the way that each sample is encoded (i. e. , the bin boundaries), but also by the number of spatial samples rspat and the number of temporal samples rtemp. Specifically, S (n bits; r spat, r temp), (6) denotes an encoding strategy that uses nbits to discretize odor intensity, applies this discretization to rspat samples at nearby locations obtained at rtemp points in time. Note that the number of bins used to discretize odor concentration is given by 2 n bits. When investigating strategies with two sensors (rspat = 2), we take two samples at a distance of 0. 3 cm (four pixels) centered around the locations specified in Eq (2). For sampling strategies specified by the notation of Eq (6), bin boundaries are obtained by histogram equalization. To indicate that the “greedy” strategy has been used for obtaining bin boundaries, we use the symbol n bits *. The total number of bits used for encoding a sample m is given by nbits ⋅ rspat ⋅ rtemp (or n bits * · r spat · r temp). To ensure that our results do not reflect the idiosyncrasies of odor concentrations at specific locations, all calculations were repeated after jittering the grid location. Specifically, the grid was rigidly moved from its standard location (as given in Eq (2) ) by 0. 74–2. 22 mm (1-3 pixels) in x and y directions, yielding a total of 49 placements. In all figures of the results section, mutual information at these jittered locations are shown as shaded blue and green regions.
We considered encoding schemes that probed the three basic ways in which resources could be allocated to encoding the odor measurements: for resolving concentration, for sampling across space, and for sampling across time. Here and in the other analyses below, parallel calculations were carried out for three odor environments: fast flow (A), slow flow (B) and boundary flow (C), and for two sets of locations (narrow grid (blue) and wide grid (green) ) within each environment. The fast flow and boundary flow conditions have the fastest inlet flow of 10 cm/s, but the boundary flow dataset was taken near a boundary where the odor surrogate’s dynamics are affected by boundary layer effects. Hence, boundary flow is the condition were diffusion has the biggest impact; see Methods for details. As a consequence of the more diffusive regime of the boundary flow condition the mutual information values we obtained for this condition are somewhat higher than in the other two conditions. The slow flow dataset has an inlet velocity of 5 cm/s. Except as noted, the analyses with different datasets and different grid choices yielded similar results. Fig 3A1–3C1 shows results for strategies that devote all bits to encoding concentration at one point in space and time (S (n bits; 1,1) ). As the resolution for odor concentration increases, so does MI, but only up to a point: once four bits are used to resolving odor concentration, additional resolution yields only minimal increases in MI. When measurements are made at two sensor locations (transversely separated by 0. 3 cm), using additional bits for coding allows MI to increase beyond the plateau encountered with a single sensor (Fig 3A2–3C2). The benefit of spatial sampling is not merely the result of having two independent samples. Specifically, MI computed after ignoring which sample corresponded to which sensor was smaller, by up to 0. 1 to 0. 2 bits (dashed curves in Fig 3A2–3C2), than the MI conveyed by a coding scheme that keeps track of which sample is which. This indicates that sampling with two sensors enables extraction of a spatial feature of the odor plume that varies along the vertical axis. This trend is also true for different spacing between two sensors, as shown for half intersensor distance and double intersensor distance in S5 Fig. Note that in the boundary flow condition, the curves continue to increase rapidly at the limits of measurement, suggesting that MI is not close to saturation. Encoding odor measurements at two consecutive times (separated by 1. 6 s) also increases MI beyond the plateau of a single sample, but not by as much as for two spatial samples (Fig 3A3–3C3). While each additional bit used for resolving the concentration of two consecutive samples provides greater MI, the increases become progressively less, suggesting that MI has reached a plateau when five bits of resolution are devoted to two samples separated in time. Virtually identical results are obtained for longer intervals between samples; this is expected since MI reaches an asymptotic value as a function of sampling interval (see section temporal encoding strategies below). In the above analysis, we discretized the odor concentration into sub-intervals of equal probability, as this histogram-equalization procedure provides the greatest amount of information about the odor concentration itself [18,20]. However, this does not yield the maximal MI about location, so we carried out a further analysis that explored the discretization strategy. For the simple case of discretization into two levels, we show how the MI depends on the binarization threshold in Fig 4. For the boundary flow condition (C) the information curves are flat over a large range for the narrow grid, and has a maximum above the median for the wide grid. For the fast flow (A) and slow flow (B) condition the maximum of information is obtained when the threshold is above the median for both grids. This suggests the most informative samples about location occur at high concentration. A threshold above the median exploits this feature of the odor statistics and allows better discriminability between locations. A comparison between the bin boundaries obtained by histogram-equalization and the optimal bin boundary when binarizing odor can be seen in S2 Fig. It is evident that the optimal bin boundary occurs at a higher concentration than the median for all but the narrow grid of the most diffusive condition. To investigate how a different choice of bin boundaries affects the results of Fig 3, we implemented a “greedy” partitioning scheme (see Methods) in which the first cutpoint was chosen to yield the maximal MI about location, and then successive cutpoints were chosen so that each maximized the MI about location, given the previous partitioning. Results (see S3 Fig) were very similar to the above analysis based on histogram-equalized bins (Fig 3). Although one- and two-bit encoding schemes (two to four partitions) yielded more MI than histogram equalization, the plateau seen in row 1 of Fig 3 was essentially unchanged. The advantage of encoding schemes based on two spatial or two temporal samples persisted. The above findings show that overall, there is surprisingly little benefit to allocating coding bits to resolving odor concentration, compared to allocating them to capture several samples across space or time. We hypothesized that resolution of odor concentration might become more important in regimes that were more diffusive, especially when coupled with sampling at two locations. To investigate this hypothesis, we compared coding schemes in which the same number of bits (four bits at each of two spatial samples) were allocated to one, two, or four samples in time, and in which the spatial sampling was across the flow axis (as in Fig 3), or along the flow axis. Fig 5 shows that this hypothesis is supported. Considering first bin boundaries based on histogram equalization, and sensor locations across the flow axis (unshaded portions of plots in first row of Fig 5), two or more bits were only beneficial for the most diffusive environment boundary flow (Fig 5C). Likewise, for sensor locations along the flow axis (shaded half of each subplot), more than one bit of resolution was only helpful in this environment (boundary flow (Fig 5C) ). Similar conclusions are reached when bin boundaries are determined via the “greedy” binning procedure: more than one bit of resolution for odor concentration is only useful in the most diffusive environment (boundary flow (Fig 5C) ), and has the greatest benefit when the two sensors are across to the axis of flow. In the fast flow condition, increasing resolution while decreasing the number of samples in time makes little difference (Fig 5A), and for the slow flow condition (Fig 5B), increasing resolution while decreasing the number of samples leads to a loss of information about location for either sensor orientation. In sum, the results of Figs 4C, 5C1 and 5C2 show that in a diffusive regime the exact choice of bin boundaries is not important, but devoting up to four bits to concentration resolution has a benefit over accumulating multiple temporal samples. When the flow conditions are more turbulent, a navigator benefits from classifying multiple odor samples at coarser resolution (Fig 5A and 5B), but the choice of the discretization threshold becomes important (Fig 4A and 4B). Consistent across conditions, sampling across the odor plume yielded more MI than sampling along the mean flow direction (white vs. gray shaded regions in Fig 5).
We now discuss the implications of our findings, first with regard to sensation and then with regard to navigation algorithms. As a starting point, we consider the simple scenario of a sensory system confronted with a continuous and widely varying input, but limited in the number of symbols that it can use for encoding. As is well-known, information is maximized when each of the symbols is used equally often, i. e. , histogram equalization. Histogram equalization can be implemented as a nonlinearity applied to the input prior to producing a neural output [18]. For a positively skewed distribution, such as light intensities or odor intensities, the nonlinearity is a highly compressive one, so that it takes into account the rarity of very large inputs. Here, however, we consider the task of maximizing information not about the sensory signal itself, but about location—which is related to odor concentration in a complex, stochastic manner. As we showed, most of the available information about location can be conveyed by a coarse discretization of the sensory range—in fact, by binarization. However, this only holds if the cutpoint is properly chosen. In the two more turbulent odor environments considered here, the optimal cutpoint is substantially higher than the median, which is the cutpoint associated with histogram equalization (see Fig 4). That is, discriminations in the upper range of odor concentrations play a disproportionately greater role in determining location, than in reconstructing the input per se. Correspondingly, implementation of this encoding requires a nonlinearity that is less compressive for higher intensities than histogram equalization. Optimal adaptation strategies, in the sense of being maximally informative, under naturalistic stimuli are (to our knowledge) unknown. The problem of optimally discretizing a signal is not just an olfactory problem but applies to other sensory modalities which face resource constraints as well (e. g. vision [26–28]). While it is difficult to imagine a biologically-plausible mechanism that achieves the precisely optimal nonlinearity for conveying information about location, there is a simple and plausible mechanism that can achieve an approximation: ligand-receptor binding in olfactory receptor neurons [29]. In steady-state, this mechanism generates a nonlinear encoding described by the Hill equation [30]. This transformation compresses signals at high concentrations, because receptors become occupied, and more ligand is required to activate the remaining receptors [31]. Thus, the degree of compression depends on the apparent dissocation constant Kd, the odorant concentration at which half of the receptors are occupied. Setting Kd at the median odor concentration corresponds to histogram equalization: half of the time the ligand binding will be below the median, and half of the time it will be above. Interestingly, setting Kd at the mean concentration, rather than the median, leads to less compression than histogram equalization. This is because the measured odor concentrations are positively skewed. Since the mean odor concentration is larger than the median, this setting will produce a response that is less than half-maximal most of the time. Such a coding strategy results in more information about location than histogram equalization, as we have outlined above (see Fig 4). In order to implement this strategy, olfactory receptors or receptor neurons would have to have an apparent Kd close to the mean concentration in the environment. Adaptation of Kd to the mean has been observed in olfactory receptor neurons of the fruitfly [32–34], and might serve to increase the amount of information that the fly olfactory system can encode about its location in a turbulent environment. With regard to odor navigation algorithms, we note that these fall into two categories: those that rely on local cues (e. g. comparison of concentration differences in two sensors [35], comparison of sample arrival times in two sensors [13], the combination of local anemotactic and olfactory cues [36,37]), and those algorithms that construct a cognitive map (like infotaxis [1] and mapless [2]). We do not intend to argue for one kind of strategy over the other, but rather to identify aspects of the odor navigation problem that apply to both, as both begin with the acquisition of sensory samples. Our work suggests that these algorithms can operate on a coarse representation of odor concentration since we find that a four-bit representation of the odor intensity reveals almost the same amount of information as finer odor concentration representation. We also found that sampling with two sensors adds substantially to the amount of information about location, and this improvement is not just due to obtaining two samples, but by comparing them in a labelled fashion (as observed in the second row of Fig 3). While this is directly exploited by comparison algorithms using two sensors, we suggest that, navigation algorithms that use an internal model of the odor distribution like infotaxis and mapless could also be improved by incorporating measurements from two sensors. Finally, an important caveat of our study is that animals have multi-sensory cues available; here we only consider the single modality of odor and do not integrate information of other modalities, e. g visual or mechanosensory flow information, that navigators have access to. In particular, it is crucial for moths and fruitflies to combine flow information via mechanosensory input when walking and visual input when flying for successful navigation [38–41]. For example, since the wind direction may meander substantially, a simple upwind movement can lead a navigator out of the odor plume [8,42]. Simultaneously recording flow and odor concentration, and analysis along the lines undertaken here, may shed light on useful sampling strategies for combining both sources of information. Determining the location of an odor source based on olfactory cues is a challenging problem. We focused on how to optimally sample from the odor distribution when the goal is to determine location with respect to the source. This study shows that the sampling strategy that maximizes information about location under finite resources utilizes two sensors, allowing for the comparison of spatially separated samples, while representing odor concentration in no more than three to four bits. Furthermore, temporal sequences of samples can be averaged to preserve resources while only minimally affecting the amount of information that the sequence conveys.
Navigating towards a food source or mating partner based on an animals’ sense of smell is a difficult task due to the complex spatiotemporal distribution of odor molecules. The most basic aspect of this task is the acquisition of samples from the environment. It is clear that odor concentration does not vary smoothly across space in many natural foraging environments. Using data from three different naturalistic environments, we compare different sampling strategies and assess their efficacy in determining the sources’ location. Our findings show that coarsely encoding the concentration of samples at separate sensors and/or multiple times provides more information than encoding fewer samples with higher resolution. Furthermore, coding resources should be focused on discriminating rare high-concentration odor samples, which are very informative about the sampling location. Such a nonlinear transformation can be implemented biologically by the receptor binding kinetics that bind odorants as a first stage of the sampling process. A further implication is that animals as well as computational models of algorithms can operate efficiently with a coarse representation of the odor concentration.
classical mechanics
chemical compounds
fluid mechanics
quantum tunneling
neuroscience
organic compounds
turbulence
probability distribution
animal behavior
mathematics
odorants
materials science
zoology
quantum mechanics
thermodynamics
entropy
animal cells
behavior
materials by attribute
chemistry
fluid dynamics
olfactory receptor neurons
probability theory
continuum mechanics
physics
animal migration
cellular neuroscience
acetones
organic chemistry
cell biology
animal navigation
neurons
biology and life sciences
cellular types
physical sciences
afferent neurons
Information-theoretic analysis of realistic odor plumes: What cues are useful for determining location?