2112 00559 Two-scale tools for homogenization and dimension reduction of perforated thin layers: Extensions, Korn-inequalities, and two-scale compactness of scale-dependent sets in Sobolev spaces

Visualization of germlayer formation requires fast and minimally invasive imaging with cellular resolution over hours. We built a custom 4-lens Selective Plane Illumination Microscopy (SPIM) setup19 capable of performing multi-view imaging of the triply labeled embryos with high acquisition speed (~30 s per time point), achieving cellular-resolution across the entire zebrafish embryo from 4–18 hpf. In order to limit the acquisition to relevant data only and thereby eliminate non-informative background in real-time, we acquired a 300 µm thick spherical shell around the embryo surface every 150 s (Supplementary Fig. 3). So only about 50% of the data needed to be transferred, stored and analyzed, while still faithfully capturing the 3D nature of germlayer formation.

Aside from analyses that characterize relationships between these two scales of activity, there are also efforts to leverage information from both scales in unison to learn something about behavior or cognition. Two distinct modeling approaches have been developed to interpret neural activity principally from spikes and LFPs, including statistical modeling and biophysical modeling. With regard to statistical modeling, earlier methods leveraged spiking and LFP activities from similar timescales in the same models [25, 33, 34].

3. Multidimensional Scaling

While both imaging modalities provide functional measures of neural activity, they offer distinct advantages. Combining these two modalities enables the study of how BOLD activation relates to neurotransmitter release, which is particularly powerful when linking these measures to a particular behavior or investigating an intervention [14, 149, 217–221]. Multi-scale analysis methods for ECoG and intracortical recordings are similar to those of spike-LFP.

multi-scale analysis tools

Their model can adaptively and separately update parameters at different rates for LFPs and spikes in closed-loop simulations. On the other hand, some studies modeled spikes and LFPs in a biophysical manner, where they aimed to identify the neural sources that contribute to the recording patterns in spikes or LFPs [21, 94, 180]. For example, the integrate-and-fire neuron model [186, 187] and its derivative, the leaky integrate-and-fire (LIF) model [188], are commonly used to describe spiking neurons and study brain functions. Moreover, Mazzoni et al successfully predicted LFPs from the LIF model and provided a simple formula that could quantitatively link neural models and LFP measurements [189]. Complex spatiotemporal neural activity encodes rich information related to behavior and cognition. Conventional research has focused on neural activity acquired using one of many different measurement modalities, each of which provides useful but incomplete assessment of the neural code.

Methodology for mapping the national ecological network to mainland Portugal: A planning tool towards a green infrastructure

The cell perimeter is computed as the sum of the lengths of all bonds belonging to the cell boundary. The length of a bond is computed as the summed pixel distance going along this bond pixel by pixel. In particular, when advancing on pixel up, down, left, or right, one is added to the bond length. E, “Stochastic
models of polymeric fluids at small Deborah number,” submitted to J. One technique used to account for microstructural nuances is to use an analytical equation to model behavior. Engineers develop these equations empirically by witnessing controlled experiments.

multi-scale analysis tools

Solving each scale individually and linking their results is much faster than trying to solve a single high-resolution model containing all relevant details. The growth of multiscale modeling in the industrial sector was primarily due to financial motivations. From the DOE national https://wizardsdev.com/en/news/multiscale-analysis/ labs perspective, the shift from large-scale systems experiments mentality occurred because of the 1996 Nuclear Ban Treaty. At LANL, LLNL, and ORNL, the multiscale modeling efforts were driven from the materials science and physics communities with a bottom-up approach.

Supplementary Video 5

Almost all filters are based on some scale parameter, be it the size of the filtering kernel in the case of linear filters (Gonzales and Wintz, 1987), structuring element (Serra, 1982), or time in the case of Partial Differential Equation (PDE)-based methods. The entire concept of multiscale analysis hinges on the notion of scale (Bangham et al., 1996c; Jackway and Deriche, 1996; Koenderink, 1984; Perona and Malik, 1990). In many cases, such as vessel enhancement (Agam et al., 2005; Du and Parker, 1997; Frangi et al., 1998; Sato et al., 1998; Wilkinson and Westenberg, 2001), the objects are characterized by shape rather than size. Usually, this requires multiple applications of a single filter at different scales and recombination of the results (Du and Parker, 1997; Frangi et al., 1998; Sato et al., 1998). Alternatively, a complex method to determine the local scale is used (Agam et al., 2005). MiBiOmics aims to provide established and novel techniques to reveal robust signatures in high dimensional datasets [13] through a graphical user interface allowing to perform widely applicable multi-omics analyses for the detection and description of associations across omics layers.

multi-scale analysis tools

Computational pathology is the computational analysis of digital images obtained through scanning slides of cells and tissues (van der Laak et al., 2021). Their success relies on automatically learning the relevant features from the input data. However, usually, CNNs cannot easily handle the multi-scale structure of the images since they are not scale-equivariant by design (Marcos et al., 2018; Zhu et al., 2019) and because of WSI size.

7. Beyond single-scale analyses

Each nematic is assigned a position on the tissue that corresponds to the center of combined mass of the two daughter cells. To visualize division orientation patterns, unit nematics can be added within different regions and averaged over different time intervals (Figure 3D, Video 10, TMR-User Manual section 2.9). To visualize both the magnitude and direction of cell elongation, we represent the elongation nematic as a line whose length and angle correspond to the magnitude and angle of cell elongation, respectively.

  • We then present our case for integrating activity across multiple scales to benefit from the combined strengths of each approach and elucidate a more holistic understanding of neural processes as well as more robust strategies for decoding information from the brain.
  • For example, this ‘fusion’ approach has been applied to asynchronously collected MEG and fMRI data to identify temporally and spatially precise signatures of human object recognition [39].
  • Snakemake automatically builds a directed graph from which the execution order of processing steps is inferred.
  • ROI definition allows the user to define morphologically relevant regions of interest and compare the behavior of cells in the different regions.

The equivariance property of a transformation means that when a transformation is applied, it is possible to predict how the representation will change (Lenc and Vedaldi, 2015; Tensmeyer and Martinez, 2016). This is not normally true for CNNs, because if a scale transformation is applied to the input data, it is usually not possible to predict its effect on the output of the CNN. The knowledge about the scale is essential for the model to identify diseases, since the same tissue structures, represented at different scales, include different information (Janowczyk and Madabhushi, 2016). CNNs can identify abnormalities in tissues, but the information and the features related to the abnormalities are not the same for each scale representation (Jimenez-del Toro et al., 2017).

A user-friendly data-mining library to easily collect information for comparing multiple datasets

One variant of this approach uses condition-specific connectivity estimates from psychophysiological interaction models to train cross-validated SVMs. This approach revealed reward identity specific connectivity patterns of the central orbitofrontal cortex [141]. Specifically, the predictions of rewarding sweet and savory odors were differentially related to olfactory (i.e. piriform) cortex.

In the tracked-cell mask, all pixels inside the cell circumference have the same unique color. If a cell is blue, it is a daughter cell that emerged from a division between two consecutive frames. Cell contact dynamics can be viewed directly on movies of tissue morphogenesis by assigning colors to cells as they gain (red) or lose (green) contacts. Those cells that simultaneously gain and lose different cell contacts are colored blue (Figure 4B–B’).


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