Origin Dilation
Origin Dilation - Related Videos
07:45
Quantifying Intermembrane Distances with Serial Image Dilations
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Cited by 11 •
2018
The purpose of this algorithm is to continuously measure the distance between two 2-dimensional edges using serial image dilations and pathfinding. This algorithm can be applied to a variety of fields such as cardiac structural biology, vascular biology, and civil engineering.
01:26
Origin of Photosynthesis
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2026
Photosynthesis represents a fundamental biological process that transformed Earth's atmosphere and paved the way for complex life. Emerging roughly 3.4–3.8 billion years ago, the earliest photosynthetic organisms harnessed light energy to produce organic compounds. These anoxygenic phototrophs used electron donors like hydrogen sulfide (H₂S) or ferrous iron (Fe²⁺), rather than water, and did not release molecular oxygen (O₂) as a byproduct. Various groups, including green sulfur and purple...
05:14
A Doxorubicin-Induced Murine Model of Dilated Cardiomyopathy In Vivo
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Cited by 9 •
2020
Described is a protocol to establish a Doxorubicin-induced dilated cardiomyopathy (DCM) model in mice via long-term intraperitoneal injection of Doxorubicin.
01:30
Cardiomyopathy II: Dilated Cardiomyopathy
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2025
Dilated cardiomyopathy, or DCM, is a progressive myocardial disorder characterized by ventricular chamber dilation and contractile dysfunction.EtiologyVarious factors can cause DCM, including hypertension and heavy alcohol intake, which contribute to the weakening and enlargement of the heart muscle. Viral infections, such as Coxsackievirus B, adenoviruses, and influenza, can lead to DCM by causing inflammation and damage to heart tissue. Certain chemotherapeutic agents, including daunorubicin,...
01:24
Origin of Cellular Life
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2026
The origin of life on Earth is a complex and enigmatic event rooted in ancient biochemical processes and geological conditions. Experimental evidence supports the hypothesis that life began with the spontaneous formation of organic molecules such as RNA nucleotides, amino acids, and lipids under early Earth conditions. Factors like volcanic activity, intense UV radiation, and a reducing atmosphere without free oxygen likely facilitated these reactions. Hydrothermal vents on the ocean floor are...
FAQs
The coordinate rule gives a direct algebraic test: multiply both coordinates of every point by k, rather than changing only one coordinate. Using the same multiplier for x and y preserves each point’s direction from the origin when k is positive, while changing its distance consistently. This connects the geometric transformation to a simple point-by-point calculation.
A negative scale factor reverses the placement of the image across the origin instead of preserving each point’s direction. The magnitude of the factor still controls how far the image lies from the origin, while the negative sign determines the opposite-side position. This distinction allows coordinate rules to describe both size change and directional reversal.
Scaling both coordinates by the same factor preserves angle measures and the overall shape of the figure. The lengths change, and the area changes as a consequence of that scaling, but the figure remains a similar version of the original. This makes the transformation useful for studying proportional size changes without altering geometric form.
First, identify the scale factor and list the coordinates of the figure’s points. Next, multiply both coordinates of each point by that factor to obtain the image coordinates. Finally, plot the resulting points and connect them in the original order. Checking the image’s position relative to the origin and its changed size helps confirm the transformation.
Compare corresponding points in the original figure and its image, focusing on their distances from the origin. If every distance changes by the same multiplier, that common multiplier is the scale factor. A positive factor indicates preserved direction from the origin, whereas a negative factor indicates placement on the opposite side. This provides a coordinate-based way to analyze similarity.
Origin dilations help model scale, construct similar figures, and connect algebraic rules with geometric effects. A coordinate equation can therefore describe an enlargement or reduction while the plotted image shows the corresponding spatial change. In mathematics, this connection supports analysis of transformations, similarity, lengths, areas, and the relationship between numerical factors and visual geometry.