Spatial Regions
Spatial Regions - Related Videos
08:52
Spatial Molecular Imaging of the Glycome Using Mass Spectrometry
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Cited by 1 •
2025
This protocol details the key steps to enable rigorous and reproducible measurement of both glycogen and N-linked glycans using mass spectrometry imaging.
07:51
Spatial Cueing
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2023
Source: Laboratory of Jonathan Flombaum—Johns Hopkins University Attention refers to the limited human ability to select some information for processing at the expense of other stimuli in the environment. Attention operates in all sensory modalities: vision, hearing, touch, even taste and smell. It is most often studied in the visual domain though. A common way to study visual attention is with a spatial cueing paradigm. This paradigm allows researchers to measure the consequences of focusing...
10:16
Mining Spatial Transcriptomics Datasets using DeepSpaceDB
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2025
This article introduces a protocol for using DeepSpaceDB, a dynamic, interactive database for spatial transcriptomics, offering analysis workflows and examples to explore tissue organization and disease-related gene expression.
10:37
Spatial Separation of Molecular Conformers and Clusters
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Cited by 3 •
2014
We present a technique that allows the spatial separation of different conformers or clusters present in a molecular beam. An electrostatic deflector is used to separate species by their mass-to-dipole moment ratio, leading to the production of gas-phase ensembles of a single conformer or cluster stoichiometry.
01:03
IR Frequency Region: Fingerprint Region
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2024
IR spectra are divided into two main regions: the diagnostic region and the fingerprint region. The diagnostic region of the spectrum lies above 1500 cm−1. The absorptions resulting from single-bond vibrations of the N–H, C–H, and O–H stretch at higher wavenumbers and appear on the left side of the spectrum. The stretching absorptions of the C≡C and C≡N occur between 2100–2300 cm−1. In contrast, those arising from stretching absorptions of the C=O, C=N, and C=C occur between 1600–1850 cm−1. The...
FAQs
The choice between a strict inequality and a non-strict inequality determines whether the boundary belongs to the spatial region. A strict condition excludes points satisfying the boundary equation, while a non-strict condition includes them. This distinction matters when classifying points as inside or outside and when describing the exact extent of a geometric domain.
An intersection retains only points shared by two or more spatial regions, so every applied condition must hold simultaneously. A union includes points belonging to at least one region, allowing separate areas to be treated as one set. These operations let mathematical descriptions combine constraints and represent more complex domains without listing every point individually.
Boundaries separate points classified differently under the defining conditions, such as points inside and outside a domain. Equations can describe these separating locations, while inequalities identify the side or sides that belong to the region. Examining the boundary helps determine containment, intersections, and the shape of the resulting geometric set.
Coordinates, equations, inequalities, and set notation emphasize different aspects of the same domain. Coordinates identify locations, equations specify relationships among coordinates, and inequalities select points satisfying one-sided constraints. Set notation records membership directly. Choosing among these forms depends on whether the goal is visualization, classification, geometric analysis, or combining conditions.
First identify the relevant coordinates and the geometric or physical constraints. Express boundary relationships with equations, then use inequalities to select the intended side or interior. Record the resulting set and combine separate conditions through intersections or unions. Finally, inspect the boundary and representative points to check that the classification matches the intended region.
A larger domain can be divided into spatial regions whose boundaries make the geometry easier to describe. Each subregion can then be represented with suitable coordinates, equations, or inequalities, allowing integration to be organized over simpler pieces. This approach supports the analysis of areas, volumes, and other quantities associated with geometric domains.
Plotting equations and inequalities makes the locations of boundaries and the distribution of included points visible. In geometry, this reveals shapes, distances, and relationships; in calculus, it helps display domains and solution sets. The same framework can model portions of physical space by assigning mathematical conditions to the locations that belong to each region.