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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.

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.

Chromosomal translocations involving the immunoglobulin heavy chain (IGH) locus define common subgroups of B-cell lymphoma but are rare in B-cell precursor acute lymphoblastic leukemia (BCP-ALL). Recent fluorescent in situ hybridization and molecular cloning studies have identified several novel IGH translocations involving genes that play important roles in normal hemopoiesis, including the cytokine receptor genes CRLF2 and EPOR, all members of the CCAAT enhancer-binding protein gene family, as well as genes not normally expressed in hemopoietic cells including inhibitor of DNA binding 4. IGH translocation results in deregulated target gene expression because of juxtaposition with IGH transcriptional enhancers. However, many genes targeted by IGH translocations are also more commonly deregulated in BCP-ALL as a consequence of other genetic or epigenetic mechanisms. For example, interstitial genomic deletions also result in deregulated CRLF2 expression, whereas EPOR expression is deregulated as a consequence of the ETV6-RUNX1 fusion. The possible clinical importance of many of the various IGH translocations in BCP-ALL remains to be determined from prospective studies, but CRLF2 expression is associated with a poor prognosis. Despite their rarity, IGH chromosomal translocations in BCP-ALL therefore define not only new mechanisms of B-cell transformation but also clinically important subgroups of disease and suggest new targeted therapeutic approaches.

Chromosomal translocations involving the immunoglobulin loci have long been recognized to play a central role in the pathogenesis of several subtypes of B-cell malignancy.18 Burkitt lymphoma is characterized by translocations involving MYC on chromosome 8q24, follicular lymphoma by involvement of BCL2 on 18q21, and mantle cell lymphoma by involvement of CCND1 on 11q13. Each translocation is present in the great majority of cases and, thus, like the Philadelphia chromosome in CML, plays an important role in disease pathogenesis. How the specificity of each type of chromosomal translocation might arise is beyond the scope of this article but presumably represents differences in the higher-order chromatin structures in B cells at different stages of differentiation.19 IGH translocations directly involve either the joining (J) or switch (S) regions of the IGH locus, regions physiologically involved in VDJ and class-switching recombination, respectively (Figure 1A). The principal consequence of IGH translocations is deregulated transcription of the translocated gene because of the physical juxtaposition of transcriptional enhancers within the IGH locus (Figure 1B). In mature B-cell malignancies, the enhancers are composed of the E enhancer lying between the IGHJ and IGHMS segments and the 2 centromeric enhancers lying distal to both IGH constant region C (IGHCA) gene segments. In normal B-cell precursors, another transcriptional enhancer, located between IGHCD and IGHG3, is also functional and contains many Ikaros transcription factor recognition motifs.20 This may be pathologically significant because approximately 5% of BCP-ALL demonstrate an interstitial deletion within the IGH locus on chromosome 14q32 with biallelic deletion of the IGHJ/IGHCM and IGHCD sequences extending to the IGHCD-IGHCG3 interval.21,22 Interestingly, Ikaros itself is also recurrently deleted in BCP-ALL, but the possible biologic and clinical consequences of these IGH deletions remain to be determined.23 Importantly, none of the IG translocations alone is sufficient for the emergence of the neoplastic phenotype; concurrent activation of synergistic oncogenes and loss of tumor suppressor gene functions are necessary.

However, we and others have shown direct involvement of CRLF2 in BCP-ALL as a consequence, not only of IGH chromosomal translocation but also more commonly as a result of an interstitial genomic deletion.17,25,26 CRLF2 maps to the pseudoautosomal regions (pseudoautosomal region 1 [PAR1]) of the short arms of both sex chromosomes; the gene maps just more than 1 Mb from the telomere. This, and the fact that the IGH locus is also at the telomere of chromosome 14q, renders the translocations cytogenetically cryptic; FISH studies are essential for detection. Both sex chromosomes are involved in translocation with IGH. The precise frequency of the IGH translocation in adolescent and adult patients remains unknown. However, in an unselected series of pediatric cases, the frequency of the translocation was 0.8%. The consequences of CRLF2/IGH translocation are deregulated expression of CRLF2 at the cell surface.17,26

Originally reported in a single case, we have subsequently shown chromosomal translocation t(6;14)(p22;q32) to be a recurrent event in a series of 13 cases; all involve the ID4 gene on chromosome 6p22.3.12,15 The precise overall frequency and the possible prognostic and clinical significance of the ID4 translocation remain unknown, but from our initial series of cases, it may be associated with relatively good prognosis disease. All patients presented with low peripheral blood blast counts (median, 3 109/L; range, 1-11 109/L) and given the older age of most patients, most appeared to respond well to chemotherapy. However, this needs to be confirmed from prospective studies of uniformly treated cohorts of patients. Unlike both the CRLF2 and CEBP translocation cases, most ID4/IGH cases had a complex karyotype with several other structural and/or numerical chromosomal changes. A common karyotypic/FISH feature was deletion of the CDKN2A locus on chromosome 9p21 in all cases, suggesting possible synergy with ID4 dysregulation. 2351a5e196