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In geometry, a locus (plural: loci) (Latin word for "place", "location") is a set of all points (commonly, a line, a line segment, a curve or a surface), whose location satisfies or is determined by one or more specified conditions.[1][2]

The set of the points that satisfy some property is often called the locus of a point satisfying this property. The use of the singular in this formulation is a witness that, until the end of the 19th century, mathematicians did not consider infinite sets. Instead of viewing lines and curves as sets of points, they viewed them as places where a point may be located or may move.

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Until the beginning of the 20th century, a geometrical shape (for example a curve) was not considered as an infinite set of points; rather, it was considered as an entity on which a point may be located or on which it moves. Thus a circle in the Euclidean plane was defined as the locus of a point that is at a given distance of a fixed point, the center of the circle. In modern mathematics, similar concepts are more frequently reformulated by describing shapes as sets; for instance, one says that the circle is the set of points that are at a given distance from the center.[3]

Once set theory became the universal basis over which the whole mathematics is built,[6] the term of locus became rather old-fashioned.[7] Nevertheless, the word is still widely used, mainly for a concise formulation, for example:

More recently, techniques such as the theory of schemes, and the use of category theory instead of set theory to give a foundation to mathematics, have returned to notions more like the original definition of a locus as an object in itself rather than as a set of points.[5]

Other examples of loci appear in various areas of mathematics. For example, in complex dynamics, the Mandelbrot set is a subset of the complex plane that may be characterized as the connectedness locus of a family of polynomial maps.

To prove a geometric shape is the correct locus for a given set of conditions, one generally divides the proof into two stages: the proof that all the points that satisfy the conditions are on the given shape, and the proof that all the points on the given shape satisfy the conditions.[10]

In the figure, the points K and L are fixed points on a given line m. The line k is a variable line through K. The line l through L is perpendicular to k. The angle {\displaystyle \alpha } between k and m is the parameter.k and l are associated lines depending on the common parameter. The variable intersection point S of k and l describes a circle. This circle is the locus of the intersection point of the two associated lines.

This week, researchers from the DNA testing company 23andMe published a paper in Nature Genetics suggesting that those infected with the virus who possess a certain genetic locus were 11 percent more likely to lose their sense of taste or smell.

For small to mid-sized rooms at middle-to-mildly loud volumes, bookshelf speakers stand at the locus between price, footprint, and performance, while also presenting an enormous amount of options in the price range, design, and features.

In geometry, the set of all points (and only those points) that satisfy certain conditions; these points form a curve or figure. For example, the locus of all points in space one foot from a given point is a sphere having a radius of one foot and having its center at the given point. The locus of all points in a plane one foot from a given point is a circle having a radius of one foot and having its center at the given point.

Would rather have something that can be controlled parametrically where can I find an explanation of how to generate xyz locus, where x and y can be controlled as I would in gh2 using range and grafting on either x or y?

Locus ceruleus (LC)-supplied norepinephrine (NE) suppresses neuroinflammation in the brain. To elucidate the effect of LC degeneration and subsequent NE deficiency on Alzheimer's disease pathology, we evaluated NE effects on microglial key functions. NE stimulation of mouse microglia suppressed Abeta-induced cytokine and chemokine production and increased microglial migration and phagocytosis of Abeta. Induced degeneration of the locus ceruleus increased expression of inflammatory mediators in APP-transgenic mice and resulted in elevated Abeta deposition. In vivo laser microscopy confirmed a reduced recruitment of microglia to Abeta plaque sites and impaired microglial Abeta phagocytosis in NE-depleted APP-transgenic mice. Supplying the mice the norepinephrine precursor L-threo-DOPS restored microglial functions in NE-depleted mice. This indicates that decrease of NE in locus ceruleus projection areas facilitates the inflammatory reaction of microglial cells in AD and impairs microglial migration and phagocytosis, thereby contributing to reduced Abeta clearance. Consequently, therapies targeting microglial phagocytosis should be tested under NE depletion.

MLVA, an abbrevation for multiple locus variable number of tandem repeats analysis, is another technique used by microbiologists to generate a DNA fingerprint or a bacterial isolate. Microbiologists usually perform MLVA after they have performed Pulsed-Field Gel Electrophoresis (PFGE) so they can get more details about the type of bacteria that may be causing an outbreak.

Most people have either an internal or external locus of control. Those with an internal locus of control believe that their actions matter, and they are the authors of their own destiny. Those with an external locus of control attribute outcomes to circumstances or chance.

Julian B. Rotter developed the locus of control concept in 1954, and it continues to play an important role in personality studies. In 1966, Rotter created a 13-item forced-choice scale in order to measure locus of control, though it is neither the only nor the most popular scale in use today.

People with high self-efficacy and an internal locus of control tend to cope better with stress, because they feel like their actions make a difference. Meanwhile, those with an external locus of control or lower levels of self-efficacy are prone to feelings of helplessness, resulting in the excess release of the stress hormone cortisol. This, in turn, can lead to a sense of hopelessness and depression.

Hovenkamp-Hermelink JHM, Jeronimus BF, van der Veen DC, et al. Differential associations of locus of control with anxiety, depression and life-events: A five-wave, nine-year study to test stability and change. J Affect Disord. 2019;253:26-34. doi:10.1016/j.jad.2019.04.005

The concept of Locus of Control of Reinforcement was developed by Julian B. Rotter. He was an American psychologist who specialized in social learning theory. He first published a paper outlining the locus of control in 1966.

But what do studies say about the internal locus of control when it comes to gender differences? On this topic, not all researchers came to the same conclusion. Some studies show that the internal locus of control is more common in men than women. But other studies say the opposite.

External locus of control means that control stems from external forces. When you have an external locus of control, you believe that events outside of your control drive your actions and the outcomes you get.

According to several studies, having an external locus of control as a main driving force correlates with several risks for criminal or problematic behavior. Studies also suggest that those with an external locus of control are less open to engaging in treatment than those with an internal locus of control.

For example, someone with a strong internal locus of control may be very direct and to the point. While this can make for clear communication in the workplace, it can also lead to a lack of tact. It can be easy to steamroll over others who are less direct.

Someone with a high internal locus of control may also find it difficult to delegate. Once they delegate, things are no longer under their control. Putting this much importance on control can also lead to burnout. Because they believe everything they want to achieve relies on them, the slope toward overworking can be slippery. This can take a toll on mental health and self-esteem.

On the other hand, there can be several positive aspects to having an external locus of control. For instance, these people may be more sensitive to their surroundings and more perceptive of others on the team, potentially making them better team players.

Genes have pairs of alleles (one from each parent) that are located at specific sites (loci) on a chromosome. When dogs breed, the mother and father each randomly contribute one allele from each locus, giving each allele a 50% chance of being passed on to the pups. One of the alleles at each locus is dominant and determines the traits, like coat color, portrayed in the dog.

B (brown) locus. This locus is linked to brown, chocolate, and liver. There are two brown alleles, B (dominant brown) and b (recessive brown). It takes two recessives (bb) to dilute black pigment to brown. For dogs in the red or yellow pigment family (phaeomelanin), the brown allele can change the color of the nose and foot pads to brown.

D (dilute) locus. This genetic site is responsible for diluted pigment which lightens coats from black or brown to gray or blue or very pale brown. A mutation in the melanophilin (MLPH) gene is the cause of color dilution. The two alleles associated with dilution are D (dominant full color) and d (recessive dilute). It takes two recessives (dd) to lighten black pigment to gray or blue and red pigment to cream.

M (merle) locus. The mutation that causes merle in all its forms has been identified. This site creates coats of irregularly shaped patches of diluted pigment and solid color. Merle only dilutes eumelanin (black) pigment. Dogs with red or yellow pigment are not merle but can produce merle pups. 2351a5e196