Multiscale modeling Wikipedia

There is considerable evidence across neuroscientific disciplines that the brain integrates and represents information across spatial and temporal scales. In perception, information is integrated within 300–600 μm cortical columns and more than 30 distinct brain regions have been identified which together support our understanding of the visual world [265, 266]. Similarly, cascading molecular changes can modulate synaptic strength to encode memories [267]. Regarding memory, it has been recognized since the stimulation studies of Wilder Penfield that memories are widely distributed throughout the brain [268]. Contemporary theories of episodic memory argue for the integration and segregation of information distributed between the hippocampus and neocortex as central to memory organization [161, 269]. Neural oscillations exert an influence on both local and distributed neural populations and may subserve integrative functions (reviewed in [21, 270, 271]).

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  • In healthy adults, modulation of the thalamic nuclei during the retrieval of happy autobiographical memories produced changes in posterior alpha power that correlated with changes in the thalamic BOLD signal [212].
  • Additionally, a phenomenon known as ‘BMI illiteracy’ exists, in which around 15%–30% of individuals are unable to learn to control a BMI [243].
  • LFPs are thought to be generated by synchronized synaptic currents arising from hundreds of neurons and to capture key integrative synaptic processes that cannot be captured in spiking activity [21].
  • In both cases, patches are extracted with a patch size of 224 × 224 pixels without any stride.

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. 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).

Scale and landscape features matter for understanding the performance of large payments for ecosystem services

W. Zhang, “Analysis
of the heterogeneous multiscale method for dynamic homogenization problems,”
preprint. W. Zhang, “Analysis
of the heterogeneous multiscale method for elliptic homogenization problems,”
preprint. The source code for the library is available on GIT2, while the HookNet code is available here3.

multi-scale analysis tools

Multi-scale analysis of non-equilibrium hypersonic rarefied diatomic gas flow was presented by using a parallel DSMC method with the DMC model for a diatomic gas molecular collision and with the MS model for a gas-surface interaction model. The parallel implementation of the DSMC code shows to have linear scalability using the dynamic load balancing technique. The DSMC simulations revealed that the leading edge angle, gas-surface interaction effects affected on the flow over the plate, however, the three-dimensional effects would be small near the symmetric line of the plate in this flow conditions. From the three-dimensional simulations, the three-dimensional flow structure exists due to the viscous effects near the span edge.

Ecological Modelling

Homogenization methods can be applied to many other problems of this
type, in which a heterogeneous behavior is approximated at the large
scale by a slowly varying or homogeneous behavior. Several proposals have been made regarding general methodologies for
designing multiscale algorithms. The idea is to decompose the whole
computational domain into several overlapping or non-overlapping
subdomains and to obtain the numerical solution over the whole domain
by iterating over the solutions on these subdomains. The domain
decomposition method is not limited to multiscale problems, but it can
be used for multiscale problems. Even though the polymer model is still empirical, such an approach
usually provides a better physical picture than models based on
empirical constitutive laws. The most important ingredient in such a method is the Hamiltonian
which should consist of the quantum mechanical Hamiltonian for the
active region, the classical Hamiltonian for the rest as well as the
part that represents the interaction between the two regions.

multi-scale analysis tools

This LFP band was hypothesized [194] to contain information similar to low-pass-filtered spikes and had more robust chronic performance than threshold crossing spike rates. They found a robust correlation between SBP and single-unit firing rate, across changes in firing rate or recording noise level. SBP produced more accurate predictions of macaque finger movements than the threshold crossing rate feature when both inputs entered SVM decoders. These works demonstrate the power of leveraging both spikes and field potentials to yield neuroscientific insights and develop robust BMI paradigms that can translate to the clinical domain. One of the primary advantages of multi-scale and multi-modal analyses is the formation of a more complete picture of the neural processes giving rise to behavior.

4 Multi-Scale CNN for Segmentation

Understanding how to model potential longer-term dynamics and non-stationarities within ECoG signals is a recent area of work [116] and may be critical for enabling longitudinal studies and clinical neural interfaces. The growth of multiscale modeling in the industrial sector was primarily due to financial motivations. From the DOE national labs perspective, the shift from large-scale systems experiments mentality occurred because of the 1996 Nuclear Ban Treaty. Time needed to extract the patches (in seconds), varying the amount of threads, using the grid extraction method (above) and using the multi−center method (below). Number of patches extracted with the grid extraction method (above) and with the multi-center method (below), at different magnification level. In both methods, only patches from tissue regions are extracted and saved using tissue masks, distinguishing between patches from tissue regions and patches from the background.

multi-scale analysis tools

Although these markers are indirect measurements of brain activity, fMRI, fNIRS, and PET are valuable techniques due to their spatial coverage of the whole brain, non-invasiveness and clinical availability [23]. These techniques all have their own strengths and challenges, and the combination of these modalities has the potential to further clarify the neural mechanisms underlying cognitive processes and behavior. A second crucial benefit of combining data across scales and modalities is the opportunity to understand one data type with the addition of information from another.

Quantifying disorder one atom at a time using an interpretable graph neural network paradigm

These methods generally leverage new signal acquisition and processing paradigms [225, 226], and/or novel electrode designs and materials [227–229]. To the second point, invasive intracortical methods are not typically used in human subjects unless clinically motivated. For this reason, non-invasive methods (EEG, fMRI, PET) are typically leveraged in studies with healthy human subjects. On the other hand, intracortical methods are more easily implemented in animal models.

These tradeoffs limit our ability to understand behaviors which likely arise from activity across spatial and temporal scales, such as human vision and memory which are thought to occur via local and inter-areal neural activity patterns. For example, prominent theories of human episodic memory argue that it occurs through local changes in synaptic weight between neurons combined with distributed interactions between the hippocampus and neocortex [161]. It follows that with the limitations of any particular method, no single technique holds a privileged position in fully understanding memory systems, and that combinatorial methodological approaches should provide a more complete picture as compared to any method in isolation. Below, we discuss progress towards combining recording modalities to gain a richer and more complete view of how neural activity patterns across spatial and temporal scales give rise to behavior. 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.

When the system varies on a macroscopic scale, these
conserved densities also vary, and their dynamics is described by a
set of hydrodynamic equations (Spohn, 1991). In this case, locally,
the microscopic state of the system is close to some local equilibrium
states parametrized by the local values of the conserved densities. This is a way of summing up long
range interaction potentials for a large set of particles. The
contribution to the interaction potential is decomposed into
components with different scales and these different contributions are
evaluated at different levels in a hierarchy of grids.

multi-scale analysis tools

Unimodal methods each have a unique set of strengths and weaknesses (figure 1). For example, noninvasive electrophysiological methods like EEG and MEG have high temporal resolution but poor spatial resolution, and the inverse is true for fMRI, which has relatively poor temporal resolution but relatively high spatial resolution. Even an invasive method like ECoG, which has high temporal resolution and good spatial specificity, suffers from limited spatial coverage. However, high resolution in both the spatial and temporal domains is essential for building a more complete understanding of the neural processes underlying cognition.

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