2,333 research outputs found

    Parameter estimation and inference for stochastic reaction-diffusion systems: application to morphogenesis in D. melanogaster

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    Background: Reaction-diffusion systems are frequently used in systems biology to model developmental and signalling processes. In many applications, count numbers of the diffusing molecular species are very low, leading to the need to explicitly model the inherent variability using stochastic methods. Despite their importance and frequent use, parameter estimation for both deterministic and stochastic reaction-diffusion systems is still a challenging problem. Results: We present a Bayesian inference approach to solve both the parameter and state estimation problem for stochastic reaction-diffusion systems. This allows a determination of the full posterior distribution of the parameters (expected values and uncertainty). We benchmark the method by illustrating it on a simple synthetic experiment. We then test the method on real data about the diffusion of the morphogen Bicoid in Drosophila melanogaster. The results show how the precision with which parameters can be inferred varies dramatically, indicating that the ability to infer full posterior distributions on the parameters can have important experimental design consequences. Conclusions: The results obtained demonstrate the feasibility and potential advantages of applying a Bayesian approach to parameter estimation in stochastic reaction-diffusion systems. In particular, the ability to estimate credibility intervals associated with parameter estimates can be precious for experimental design. Further work, however, will be needed to ensure the method can scale up to larger problems

    Board of Dental Examiners

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    Board of Dental Examiners

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    Locally Adaptive Frames in the Roto-Translation Group and their Applications in Medical Imaging

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    Locally adaptive differential frames (gauge frames) are a well-known effective tool in image analysis, used in differential invariants and PDE-flows. However, at complex structures such as crossings or junctions, these frames are not well-defined. Therefore, we generalize the notion of gauge frames on images to gauge frames on data representations U:RdSd1RU:\mathbb{R}^{d} \rtimes S^{d-1} \to \mathbb{R} defined on the extended space of positions and orientations, which we relate to data on the roto-translation group SE(d)SE(d), d=2,3d=2,3. This allows to define multiple frames per position, one per orientation. We compute these frames via exponential curve fits in the extended data representations in SE(d)SE(d). These curve fits minimize first or second order variational problems which are solved by spectral decomposition of, respectively, a structure tensor or Hessian of data on SE(d)SE(d). We include these gauge frames in differential invariants and crossing preserving PDE-flows acting on extended data representation UU and we show their advantage compared to the standard left-invariant frame on SE(d)SE(d). Applications include crossing-preserving filtering and improved segmentations of the vascular tree in retinal images, and new 3D extensions of coherence-enhancing diffusion via invertible orientation scores

    California Coastal Commission

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    Home, head direction stability, and grid cell distortion

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    The home is a unique location in the life of humans and animals. In rats, home presents itself as a multicompartmental space that involves integrating navigation through subspaces. Here we embedded the laboratory rat’s home cage in the arena, while recording neurons in the animal’s parasubiculum and medial entorhinal cortex, two brain areas encoding the animal’s location and head direction. We found that head direction signals were unaffected by home cage presence or translocation. Head direction cells remain globally stable and have similar properties inside and outside the embedded home. We did not observe egocentric bearing encoding of the home cage. However, grid cells were distorted in the presence of the home cage. While they did not globally remap, single firing fields were translocated toward the home. These effects appeared to be geometrical in nature rather than a home-specific distortion and were not dependent on explicit behavioral use of the home cage during a hoarding task. Our work suggests that medial entorhinal cortex and parasubiculum do not remap after embedding the home, but local changes in grid cell activity overrepresent the embedded space location and might contribute to navigation in complex environments

    Absolute frequency measurements of 85Rb nF7/2 Rydberg states using purely optical detection

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    A three-step laser excitation scheme is used to make absolute frequency measurements of highly excited nF7/2 Rydberg states in 85Rb for principal quantum numbers n=33-100. This work demonstrates the first absolute frequency measurements of rubidium Rydberg levels using a purely optical detection scheme. The Rydberg states are excited in a heated Rb vapour cell and Doppler free signals are detected via purely optical means. All of the frequency measurements are made using a wavemeter which is calibrated against a GPS disciplined self-referenced optical frequency comb. We find that the measured levels have a very high frequency stability, and are especially robust to electric fields. The apparatus has allowed measurements of the states to an accuracy of 8.0MHz. The new measurements are analysed by extracting the modified Rydberg-Ritz series parameters.Comment: 12 pages, 5 figures, submitted to New. J. Phy

    Comparison of Bond Character in Hydrocarbons and Fullerenes

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    We present a comparison of the bond polarizabilities for carbon-carbon bonds in hydrocarbons and fullerenes, using two different models for the fullerene Raman spectrum and the results of Raman measurements on ethane and ethylene. We find that the polarizabilities for single bonds in fullerenes and hydrocarbons compare well, while the double bonds in fullerenes have greater polarizability than in ethylene.Comment: 7 pages, no figures, uses RevTeX. (To appear in Phys. Rev. B.

    Improving Fiber Alignment in HARDI by Combining Contextual PDE Flow with Constrained Spherical Deconvolution

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    We propose two strategies to improve the quality of tractography results computed from diffusion weighted magnetic resonance imaging (DW-MRI) data. Both methods are based on the same PDE framework, defined in the coupled space of positions and orientations, associated with a stochastic process describing the enhancement of elongated structures while preserving crossing structures. In the first method we use the enhancement PDE for contextual regularization of a fiber orientation distribution (FOD) that is obtained on individual voxels from high angular resolution diffusion imaging (HARDI) data via constrained spherical deconvolution (CSD). Thereby we improve the FOD as input for subsequent tractography. Secondly, we introduce the fiber to bundle coherence (FBC), a measure for quantification of fiber alignment. The FBC is computed from a tractography result using the same PDE framework and provides a criterion for removing the spurious fibers. We validate the proposed combination of CSD and enhancement on phantom data and on human data, acquired with different scanning protocols. On the phantom data we find that PDE enhancements improve both local metrics and global metrics of tractography results, compared to CSD without enhancements. On the human data we show that the enhancements allow for a better reconstruction of crossing fiber bundles and they reduce the variability of the tractography output with respect to the acquisition parameters. Finally, we show that both the enhancement of the FODs and the use of the FBC measure on the tractography improve the stability with respect to different stochastic realizations of probabilistic tractography. This is shown in a clinical application: the reconstruction of the optic radiation for epilepsy surgery planning
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