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Point Pattern
Point pattern analysis (PPA) is the study of ''point patterns'', the spatial arrangements of points in space (usually 2-dimensional space). The simplest formulation is a set ''X'' = where ''D'', which can be called the 'study region,' is a subset of R''n'', a ''n''-dimensional Euclidean space. Description The easiest way to visualize a 2-D point pattern is a map of the locations, which is simply a scatterplot but with the provision that the axes are equally scaled. If D is not the boundary of the map then it should also be indicated. An empirical definition of D would be the convex hull of the points, or at least their bounding box, a matrix of the ranges of the coordinates. Another straightforward way to visualize the points is a 2D histogram (sometimes called a quadrats) that bins the points into rectangular regions. A benefit of quadrat analysis is that it forces the analysis to take into account possible scales within which statistically significant inhomogeneities may be occ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2-dimensional Space
In mathematics, a plane is a Euclidean (flat), two-dimensional surface that extends indefinitely. A plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space. Planes can arise as subspaces of some higher-dimensional space, as with one of a room's walls, infinitely extended, or they may enjoy an independent existence in their own right, as in the setting of two-dimensional Euclidean geometry. Sometimes the word ''plane'' is used more generally to describe a two-dimensional surface, for example the hyperbolic plane and elliptic plane. When working exclusively in two-dimensional Euclidean space, the definite article is used, so ''the'' plane refers to the whole space. Many fundamental tasks in mathematics, geometry, trigonometry, graph theory, and graphing are performed in a two-dimensional space, often in the plane. Euclidean geometry Euclid set forth the first great landmark of mathematical thought, an axiomatic t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circle
A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant. The distance between any point of the circle and the centre is called the radius. Usually, the radius is required to be a positive number. A circle with r=0 (a single point) is a degenerate case. This article is about circles in Euclidean geometry, and, in particular, the Euclidean plane, except where otherwise noted. Specifically, a circle is a simple closed curve that divides the plane into two regions: an interior and an exterior. In everyday use, the term "circle" may be used interchangeably to refer to either the boundary of the figure, or to the whole figure including its interior; in strict technical usage, the circle is only the boundary and the whole figure is called a '' disc''. A circle may also be defined as a special ki ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Retinal Mosaic
Retinal mosaic is the name given to the distribution of any particular type of neuron across any particular layer in the retina. Typically such distributions are somewhat regular; it is thought that this is so that each part of the retina is served by each type of neuron in processing visual information. The regularity of retinal mosaics can be quantitatively studied by modelling the mosaic as a spatial point pattern. This is done by treating each cell as a single point and using spatial statistics such as the Effective Radius, Packing Factor and Regularity Index. Using adaptive optics, it is nowadays possible to image the photoreceptor mosaic (i.e. the distribution of rods and cones) in living humans, enabling the detailed study of photoreceptor density and arrangement across the retina.PLoS One. 2018 Jan 16;13(1):e0191141. doi: 10.1371/journal.pone.0191141. eCollection 2018. In the fovea (where photoreceptor density is highest) the spacing between adjacent receptors is about 6 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Infectious Disease
An infection is the invasion of tissues by pathogens, their multiplication, and the reaction of host tissues to the infectious agent and the toxins they produce. An infectious disease, also known as a transmissible disease or communicable disease, is an illness resulting from an infection. Infections can be caused by a wide range of pathogens, most prominently bacteria and viruses. Hosts can fight infections using their immune system. Mammalian hosts react to infections with an innate response, often involving inflammation, followed by an adaptive response. Specific medications used to treat infections include antibiotics, antivirals, antifungals, antiprotozoals, and antihelminthics. Infectious diseases resulted in 9.2 million deaths in 2013 (about 17% of all deaths). The branch of medicine that focuses on infections is referred to as infectious disease. Types Infections are caused by infectious agents (pathogens) including: * Bacteria (e.g. '' Mycobacterium tuberculosis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Contagious Disease
A contagious disease is an infectious disease that is readily spread (that is, communicated) by transmission of a pathogen through contact (direct or indirect) with an infected person. A disease is often known to be contagious before medical science discovers its causative agent. Koch's postulates, which were published at the end of the 19th century, were the standard for the next 100 years or more, especially with diseases caused by bacteria. Microbial pathogenesis attempts to account for diseases caused by a virus. The disease itself can also be called a contagion. Historical meaning Originally, the term referred to a ''contagion'' (a derivative of 'contact') or disease transmissible only by direct physical contact. In the modern-day, the term has sometimes been broadened to encompass ''any'' communicable or infectious disease. Often the word can only be understood in context, where it is used to emphasize very infectious, easily transmitted, or especially severe communic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Case Control Study
Case or CASE may refer to: Containers * Case (goods), a package of related merchandise * Cartridge case or casing, a firearm cartridge component * Bookcase, a piece of furniture used to store books * Briefcase or attaché case, a narrow box to carry paperwork * Computer case, the enclosure for a PC's main components * Keep case, DVD or CD packaging * Pencil case * Phone case, protective or vanity accessory for mobile phones ** Battery case * Road case or flight case, for fragile equipment in transit * Shipping container or packing case * Suitcase, a large luggage box * Type case, a compartmentalized wooden box for letterpress typesetting Places * Case, Laclede County, Missouri * Case, Warren County, Missouri * Case River, a Kabika tributary in Ontario, Canada * Case Township, Michigan * Case del Conte, Italy People * Case (name), people with the surname (or given name) * Case (singer), American R&B singer-songwriter and producer (Case Woodard) Arts, entertainment, and media ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Goodness Of Fit
The goodness of fit of a statistical model describes how well it fits a set of observations. Measures of goodness of fit typically summarize the discrepancy between observed values and the values expected under the model in question. Such measures can be used in statistical hypothesis testing, e.g. to test for normality of residuals, to test whether two samples are drawn from identical distributions (see Kolmogorov–Smirnov test), or whether outcome frequencies follow a specified distribution (see Pearson's chi-square test). In the analysis of variance, one of the components into which the variance is partitioned may be a lack-of-fit sum of squares. Fit of distributions In assessing whether a given distribution is suited to a data-set, the following tests and their underlying measures of fit can be used: * Bayesian information criterion *Kolmogorov–Smirnov test *Cramér–von Mises criterion *Anderson–Darling test * Shapiro–Wilk test *Chi-squared test *Akaike informat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ellipse
In mathematics, an ellipse is a plane curve surrounding two focus (geometry), focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. It generalizes a circle, which is the special type of ellipse in which the two focal points are the same. The elongation of an ellipse is measured by its eccentricity (mathematics), eccentricity e, a number ranging from e = 0 (the Limiting case (mathematics), limiting case of a circle) to e = 1 (the limiting case of infinite elongation, no longer an ellipse but a parabola). An ellipse has a simple algebraic solution for its area, but only approximations for its perimeter (also known as circumference), for which integration is required to obtain an exact solution. Analytic geometry, Analytically, the equation of a standard ellipse centered at the origin with width 2a and height 2b is: : \frac+\frac = 1 . Assuming a \ge b, the foci are (\pm c, 0) for c = \sqrt. The standard parametric e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Point Pattern
Point pattern analysis (PPA) is the study of ''point patterns'', the spatial arrangements of points in space (usually 2-dimensional space). The simplest formulation is a set ''X'' = where ''D'', which can be called the 'study region,' is a subset of R''n'', a ''n''-dimensional Euclidean space. Description The easiest way to visualize a 2-D point pattern is a map of the locations, which is simply a scatterplot but with the provision that the axes are equally scaled. If D is not the boundary of the map then it should also be indicated. An empirical definition of D would be the convex hull of the points, or at least their bounding box, a matrix of the ranges of the coordinates. Another straightforward way to visualize the points is a 2D histogram (sometimes called a quadrats) that bins the points into rectangular regions. A benefit of quadrat analysis is that it forces the analysis to take into account possible scales within which statistically significant inhomogeneities may be occ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
N-dimensional Space
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coordinate is needed to specify a point on itfor example, the point at 5 on a number line. A surface, such as the boundary of a cylinder or sphere, has a dimension of two (2D) because two coordinates are needed to specify a point on itfor example, both a latitude and longitude are required to locate a point on the surface of a sphere. A two-dimensional Euclidean space is a two-dimensional space on the plane. The inside of a cube, a cylinder or a sphere is three-dimensional (3D) because three coordinates are needed to locate a point within these spaces. In classical mechanics, space and time are different categories and refer to absolute space and time. That conception of the world is a four-dimensional space but not the one that was found necessa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Walk
In mathematics, a random walk is a random process that describes a path that consists of a succession of random steps on some mathematical space. An elementary example of a random walk is the random walk on the integer number line \mathbb Z which starts at 0, and at each step moves +1 or −1 with equal probability. Other examples include the path traced by a molecule as it travels in a liquid or a gas (see Brownian motion), the search path of a foraging animal, or the price of a fluctuating stock and the financial status of a gambler. Random walks have applications to engineering and many scientific fields including ecology, psychology, computer science, physics, chemistry, biology, economics, and sociology. The term ''random walk'' was first introduced by Karl Pearson in 1905. Lattice random walk A popular random walk model is that of a random walk on a regular lattice, where at each step the location jumps to another site according to some probability distribution. In a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diffusion
Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical potential. It is possible to diffuse "uphill" from a region of lower concentration to a region of higher concentration, like in spinodal decomposition. The concept of diffusion is widely used in many fields, including physics (particle diffusion), chemistry, biology, sociology, economics, and finance (diffusion of people, ideas, and price values). The central idea of diffusion, however, is common to all of these: a substance or collection undergoing diffusion spreads out from a point or location at which there is a higher concentration of that substance or collection. A gradient is the change in the value of a quantity, for example, concentration, pressure, or temperature with the change in another variable, usually distance. A change in c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
