Unsupervised landmark analysis for jump detection in molecular dynamics simulations

Molecular dynamics is a versatile and powerful method to study diffusion in solid-state ionic conductors, requiring minimal prior knowledge of equilibrium or transition states of the system's free energy surface. However, the analysis of trajectories for relevant but rare events, such as a jump of the diffusing mobile ion, is still rather cumbersome, requiring prior knowledge of the diffusive process in order to get meaningful results. In this work, we present a novel approach to detect the relevant events in a diffusive system without assuming prior information regarding the underlying process. We start from a projection of the atomic coordinates into a landmark basis to identify the dominant features in a mobile ion's environment. Subsequent clustering in landmark space enables a discretization of any trajectory into a sequence of distinct states. As a final step, the use of the smooth overlap of atomic positions descriptor allows distinguishing between different environments in a straightforward way. We apply this algorithm to ten Li-ionic systems and conduct in-depth analyses of cubic Li$_{7}$La$_{3}$Zr$_{2}$O$_{12}$, tetragonal Li$_{10}$GeP$_{2}$S$_{12}$, and the $\beta$-eucryptite LiAlSiO$_{4}$. We compare our results to existing methods, underscoring strong points, weaknesses, and insights into the diffusive behavior of the ionic conduction in the materials investigated

Orientation and Search Strategies of Desert Arthropods : Path Integration Models and Experiments with Desert Ants, <i>Cataglyphis fortis</i> (Forel 1902)

Path integration enables desert arthropods to find back to their nest on the shortest track from any position. To perform path integration successfully, speeds and turning angles along the preceding outbound path have to be measured continuously and combined to determine an internal global vector leading back home at any time. A number of experiments have given an idea how arthropods might use allothetic or idiothetic signals to perceive their orientation and moving speed. When the global vector has been run off but the nest has not yet been reached, the arthropods engage in systematic search behavior. This behavior consists of a series of search loops of ever increasing size and finally leads to a search density profile peaking at the starting location. In the theoretical part of this work, the model descriptions of mathematically precise path integration that have been developed so far are reviewed, and the hitherto not used variant of egocentric cartesian coordinates is proposed and explained. Its simple and intuitive structure is demonstrated in comparison to the previous path integration models. Measuring two quantities, forward moving speed and angular turning rate, and implementing them into a linear system of differential equations provides the necessary information during foraging run, reorientation process (e.g. at a feeding site) and return path to the nest. In addition, several possible types of systematic errors that can cause deviations from the correct homeward course are easily implemented and illustrated by means of the model. Such deviations have been observed for several species of desert arthropods in different experiments, but their origin is still under debate. The two most important error mechanisms in this respect are the Müller-Wehner-error, an approximative path integration model that accumulates systematic miscalculations in path integration whenever the animal walks different from the correct inbound and outbound direction, and the leaky integrator, a mechanism that predicts a linear underestimation of the distance to the nest with an exponential rate; both error types have been shown to occur in specific experimental paradigms with desert ants Cataglyphis fortis. Using the egocentric path integration model, simple indices are proposed that might allow to rule out or corroborate certain error types by conducting experiments. Experiments were conducted with desert ants C. fortis. Those experiments, in which natural outbound runs as well as the following inbound runs and systematic search behaviors were observed and analyzed, revealed that natural outbound runs do not differ remarkably among different ants. This holds true for their spatial conformation as well as for overall path length and distance covered during foraging. Consequently, no significant correlations between all factors determining the shape of the outbound runs and the errors that were measured via different variables for inbound run as well as systematic search were found. Besides, the extension of the systematic search does not differ remarkably. However, due to the only slight differences of the natural outbound runs, such correlations cannot be totally excluded. The error postulated by Müller and Wehner seems to be of no or minor importance during natural foraging excursions; the principle of the leaky integrator, on the other hand, might be able to explain some shortcomings of the path integration mechanism with respect to distance estimation. Repeated training increases the straightness of outbound runs. In experiments, where desert ants were trained to different distances, it became obvious that the longer the distances of foraging excursions, the larger the errors occurring during path integration (again measured via home run and systematic search), and that the ants adapt their systematic search strategy to their increasing uncertainty by extending the search pattern. Additional experiments, during which the distance was kept constant, revealed that not only the characteristics of the foraging trip influence the accuracy of path integrator and systematic search behavior, but that also nest- or route specific cues have an impact on the orientation and the systematic search patterns of desert ants. If desert ants are disturbed during their outbound runs, most of them immediately set out in direction back to the nest, even without having food in their mandibles. External cues, in the respective experiment huge landmarks placed on the route between nest and feeder, increased the number of ants that continued its preceding foraging run; but still the majority headed back towards the nest. For a number of ants successive outbound and inbound runs (ontogeny-experiment) were recorded and analyzed. As a result, their outbound runs to a known feeding site get straighter over time, whereas the inbound runs are very straight from the very beginning and no increase of their straightness could be observed. For both outbound and inbound runs also no improvement in terms of accuracy of the path integrator was found; obviously the ants perform path integration in the same fashion all the time. Even if trained to a feeder for a long time in an area free of landmarks, desert ants do not develop specific paths, as they have been observed for other species of desert arthropods

Lunar navigation study, sections 1 through 7 Final report, Jun. 1964 - May 1965

Lunar navigation analysis using passive nongyro, inertial navigation, and radio frequency technolog

Building an Allocentric Traveling-Direction Signal Via Vector Computation

Many behavioral tasks require the manipulation of mathematical vectors, but, outside of computational models, it is not known how brains perform vector operations. Here we show how the Drosophila central complex, a region implicated in goal-directed navigation, performs vector arithmetic. First, we describe a neural signal in the fan-shaped body that explicitly tracks a fly\u27s allocentric traveling angle, that is, the traveling angle in reference to external cues. Past work has identified neurons in Drosophila and mammals that track an animal\u27s heading angle referenced to external cues (e.g., head-direction cells), but this new signal illuminates how the sense of space is properly updated when traveling and heading angles differ (e.g., when walking sideways). We then characterize a neuronal circuit that rotates, scales, and adds four vectors related to the fly\u27s egocentric traveling direction––the traveling angle referenced to the body––to compute the allocentric traveling direction. This circuit operates by mapping spatial vectors onto sinusoidal patterns of activity across distinct neuronal populations, with the sinusoid\u27s amplitude representing the vector\u27s length and its phase representing the vector\u27s angle. The principles of this circuit, which performs an egocentric-to-allocentric coordinate transformation and vector addition, may generalize to other brains and to domains beyond navigation where vector operations or reference-frame transformations are required

Development of site fidelity in the nocturnal amblypygid, \u3ci\u3ePhrynus marginemaculatus\u3c/i\u3e

Amblypygids are capable of navigation in the complex terrain of rainforests in near complete darkness. Path integration is unnecessary for successful homing, and the alternative mechanisms by which they navigate have yet to be elucidated. Here, our aims were to determine whether the amblypygid Phrynus marginemaculatus could be trained to reliably return to a target shelter in a laboratory arena—indicating goal recognition—and to document changes in behavior associated with the development of fidelity. We recorded nocturnal movements and space use by individuals over five nights in an arena in which subjects were provided with two shelters that differed in quality. The target shelter, unlike the alternative shelter, shielded subjects from light in daylight hours. Individuals consistently exited and returned to a shelter each night and from the third night onward chose the target shelter more often than the alternative shelter. Indeed, on the fifth night, every subject chose the target shelter. This transition was associated with changes in movement and space use in the arena. Notably, the movement features of outbound and inbound paths differed but did not change across nights. Individuals were also characterized by distinct behavioral strategies reflecting candidate homing mechanisms

Development of site fidelity in the nocturnal amblypygid, \u3ci\u3ePhrynus marginemaculatus\u3c/i\u3e

Amblypygids are capable of navigation in the complex terrain of rainforests in near complete darkness. Path integration is unnecessary for successful homing, and the alternative mechanisms by which they navigate have yet to be elucidated. Here, our aims were to determine whether the amblypygid Phrynus marginemaculatus could be trained to reliably return to a target shelter in a laboratory arena—indicating goal recognition—and to document changes in behavior associated with the development of fidelity. We recorded nocturnal movements and space use by individuals over five nights in an arena in which subjects were provided with two shelters that differed in quality. The target shelter, unlike the alternative shelter, shielded subjects from light in daylight hours. Individuals consistently exited and returned to a shelter each night and from the third night onward chose the target shelter more often than the alternative shelter. Indeed, on the fifth night, every subject chose the target shelter. This transition was associated with changes in movement and space use in the arena. Notably, the movement features of outbound and inbound paths differed but did not change across nights. Individuals were also characterized by distinct behavioral strategies reflecting candidate homing mechanisms

Processing of sky compass cues and wide-field motion in the central complex of the desert locust (Schistocerca gregaria)

1. Polarization-sensitive neurons of the locust central complex show azimuthdependent responses to unpolarized light spots. This suggests that direct sunlight supports the sky polarization compass in this brain area. / 2. In the brain of the desert locust, neurons sensitive to the plane of celestial polarization are arranged like a compass in the slices of the central complex. These neurons, in addition, code for the horizontal direction of an unpolarized light cue possibly representing the sun. We show here that horizontal directions are, in addition to E-vector orientations from dorsal direction, represented in a compass-like manner across the slices of the central complex. However, both compasses are not linked to each other but seem to interact in a cell specific nonlinear way. Our study confirms the role of the central complex in signaling heading directions signaling and shows that different cues are employed for this task. / 3. Visual cues are essential for animal navigation and spatial orientation. Many insects rely on celestial cues for spatial orientation, including the sky polarization pattern. In desert locusts neurons encoding the plane of polarized light (E-vector) are located in the central complex (CX), a group of midline-spanning neuropils. Several types of CX neuron signalling heading direction represent zenithal Evectors in a topographic manner across the slices of the CX and, likely, act as an internal sky compass. Because animals experience optic flow stimulation during flight, we asked whether progressive wide-field motion affects the responses of CX neurons to polarized light. In most neurons, progressive motion disadapted the response to the preferred E-vector (i.e. the E-vector eliciting strongest firing), whereas the response to the anti-preferred E-vector remained comparatively unaffected. This suggests context-dependent gain modulation in sky compass signalling. Three types of compass neuron were responsive to motion simulating body rotation around the yaw axis. Depending on arborization domains in the CX and rotation direction these neurons were strongly excited or inhibited. As proposed for Drosophila, they may be involved in shifting compass signal activity across the slices of the CX as the animal turns enabling it to keep track of its heading

Generalization of navigation memory in honeybees

Flying insects like the honeybee learn multiple features of the environment for efficient navigation. Here we introduce a novel paradigm in the natural habitat, and ask whether the memory of such features is generalized to novel test conditions. Foraging bees from colonies located in 5 different home areas were tested in a common area for their search flights. The home areas differed in the arrangements of rising natural objects or their lack, and in the existence or lack of elongated ground structures. The test area resembled partly or not at all the layout of landmarks in the respective home areas. In particular, the test area lacked rising objects. The search flights were tracked with harmonic radar and quantified by multiples procedures, extracting their differences on an individual basis. Random search as the only guide for searching was excluded by two model calculations. The frequencies of directions of flight sectors differed from both model calculations and between the home areas in a graded fashion. Densities of search flight fixes were used to create heat maps and classified by a partial least squares regression analysis. Classification was performed with a support vector machine in order to account for optimal hyperplanes. A rank order of well separated clusters was found that partly resemble the graded differences between the ground structures of the home areas and the test area. The guiding effect of elongated ground structures was quantified with respect to the sequence, angle and distance from these ground structures. We conclude that foragers generalize their specific landscape memory in a graded way to the landscape features in the test area, and argue that both the existence and absences of landmarks are taken into account. The conclusion is discussed in the context of the learning and generalization process in an insect, the honeybee, with an emphasis on exploratory learning in the context of navigation