Normalization of large-scale behavioural data collected from zebrafish

Many contemporary neuroscience experiments utilize high-throughput approaches to simultaneously collect behavioural data from many animals. The resulting data are often complex in structure and are subjected to systematic biases, which require new approaches for analysis and normalization. This study addressed the normalization need by establishing an approach based on linear-regression modeling. The model was established using a dataset of visual motor response (VMR) obtained from several strains of wild-type (WT) zebrafish collected at multiple stages of development. The VMR is a locomotor response triggered by drastic light change, and is commonly measured repeatedly from multiple larvae arrayed in 96-well plates. This assay is subjected to several systematic variations. For example, the light emitted by the machine varies slightly from well to well. In addition to the light-intensity variation, biological replication also created batch-batch variation. These systematic variations may result in differences in the VMR and must be normalized. Our normalization approach explicitly modeled the effect of these systematic variations on VMR. It also normalized the activity profiles of different conditions to a common baseline. Our approach is versatile, as it can incorporate different normalization needs as separate factors. The versatility was demonstrated by an integrated normalization of three factors: light-intensity variation, batch-batch variation and baseline. After normalization, new biological insights were revealed from the data. For example, we found larvae of TL strain at 6 days post-fertilization (dpf) responded to light onset much stronger than the 9-dpf larvae, whereas previous analysis without normalization shows that their responses were relatively comparable. By removing systematic variations, our model-based normalization can facilitate downstream statistical comparisons and aid detecting true biological differences in high-throughput studies of neurobehaviour

Statistical Analysis of Zebrafish Locomotor Response

Zebrafish larvae display rich locomotor behaviour upon external stimulation. The movement can be simultaneously tracked from many larvae arranged in multi-well plates. The resulting time-series locomotor data have been used to reveal new insights into neurobiology and pharmacology. However, the data are of large scale, and the corresponding locomotor behavior is affected by multiple factors. These issues pose a statistical challenge for comparing larval activities. To address this gap, this study has analyzed a visually-driven locomotor behaviour named the visual motor response (VMR) by the Hotelling's T-squared test. This test is congruent with comparing locomotor profiles from a time period. Different wild-type (WT) strains were compared using the test, which shows that they responded differently to light change at different developmental stages. The performance of this test was evaluated by a power analysis, which shows that the test was sensitive for detecting differences between experimental groups with sample numbers that were commonly used in various studies. In addition, this study investigated the effects of various factors that might affect the VMR by multivariate analysis of variance (MANOVA). The results indicate that the larval activity was generally affected by stage, light stimulus, their interaction, and location in the plate. Nonetheless, different factors affected larval activity differently over time, as indicated by a dynamical analysis of the activity at each second. Intriguingly, this analysis also shows that biological and technical repeats had negligible effect on larval activity. This finding is consistent with that from the Hotelling's T-squared test, and suggests that experimental repeats can be combined to enhance statistical power. Together, these investigations have established a statistical framework for analyzing VMR data, a framework that should be generally applicable to other locomotor data with similar structure

Influence of Renolds number on generation and decay of aircraft wakes: Experimental investigation using generic models, F13 and F13X

The development of multiple-vortex wake systems in the far field of a generic aircraft model is assessed by evaluation of experimental data obtained from MonoPIV measurements in the large towing tank facility of the Hamburg Ship Model Basin (HSVA). In the selected experimental configurations DLR's F13X vortex generator has been operated at two geometrical configurations for three different chord-based Reynolds numbers. From the tips of the rectangular main wing a 2-vortex system shed off, and adding a horizontal tail plane to the vortex generator produced a 4-vortex system of two unequal-strength counter-rotating vortex pairs. The 2-vortex systems showed a gradual decay, its characteristic parameters have been evaluated well into the wake far field up to vortex ages of 4.5 without providing any evidence for cooperative long-wavelength instabilities. Contrarily, for the same Rec the counter-rotating vortex pairs of the 4-vortex systems underwent short-wavelength instabilities in the extended near field leading to a strong vortex interaction and rapid threedimensional reorganization. After the 'catastrophic event' only a weak 2-vortex systemremained that gradually decayed. Comparing the development of different 2-vortex systems in the given range of Rec, the behavior in the far field is Rec invariant. Also for the 4-vortex systems no distinct indication has been found for a significant Rec dependance

Towing tank PIV measurements on 2- and 4-vortex systems IGE

The present report is part of the WP 3 “Wake evolution near the ground” of the FarWake project. Experimental investigations were performed in the tow tank at Göttingen to describe spatial-temporal flow evolution of 2- and 4-vortex systems in ground effect (IGE). The F13 model consisting of one or two rectangular wings is used as vortex generator and is towed along a ground plate at specific heights h/b = 0.5, 0.25, 0.125. In case of the 4-vortex system a span width ratio of b2/b1 = 0.3 and circulation ratios of Γ2/Γ1 = ± 0.3 are considered; i.e. co- and counter-rotating vortex pairs. A Stereo Particle Image Velocimetry setup is employed to determine the flow velocity fields in a cross plane. The flow fields are analysed with respect to flow separation at the ground, the generation of secondary vortices, the spatial-temporal development of the vortex trajectories and vortex circulation

Vortex characterization in multiple-vortex systems of wing model wakes

In the wake of an aircraft large-scale vortical structures organize in multiple vortex systems with their vortex axes aligned approximately parallel to the wake axis. Equal-strength counter-rotating vortex pairs of 2–vortex wakes are known to be stable for rather high vortex ages until growing long-wavelength instabilities may lead to mutual interaction and final disintegration. Contrarily, unequal-strength counter-rotating vortex pairs eventually will grow short-wavelength cooperative instabilities and will undergo a rapid three-dimensional reorganization of the vortex system, as has recently been shown from numerical simulation [2, °3] and evidenced experimentally. By enforcing the generation of vortices that are prone to severe vortex interactions the wake vortex system could be diffused significantly faster. Such optimal perturbation by passive control of the wake could contribute to minimize aircraft separation distances necessary for air safety reason

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High-extraction coal mining in Illinois: Effects on crop production, 1985-1987

This work was sponsored by the Illinois Mine Subsidence Research Program administered by the Illinois State Geological Survey through a grant from the Coal Development Board of the Illinois Department of Energy and Natural Resources and the members of the Illinois coal industry.Ope

Experimental investigations of the influence of axial jets on 2- and 4-vortex systems

The effects of jets on wake vortices were investigated experimentally in a towing tank. Considered are two cases of 4-vortex systems consisting of two counter-rotating vortex pairs. For a comparisons, the corresponding 2-vortex system is also considered, too. The used vortex generator consisting of one or two rectangular wings was equipped with two pressurized water jet nozzles. Two different jet strengths were used, resulting in parameter valuess of R (ratio between jet thrust and vortex strength) of 0.2 and 0.74. Cross-plane velocity fields were determined by means of Stereo-PIV. The jet/vortex interactions are discussed, as well as the influence of the jets on the occurrence of an interaction between inner and outer vortices in the near far field, which is presumed to lead to a more rapid decay of the wing vortice