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An example of mildly elevated ST segments in V1 to V3 that are concave down An ST elevation is considered significant if the vertical distance inside the ECG trace and the baseline at a point 0.04 seconds after the J-point is at least 0.1 mV (usually representing 1 mm or 1 small square) in a limb lead or 0.2 mV (2 mm or 2 small squares) in a ...
A function f is concave over a convex set if and only if the function −f is a convex function over the set. The sum of two concave functions is itself concave and so is the pointwise minimum of two concave functions, i.e. the set of concave functions on a given domain form a semifield.
A: The bottom of a concave meniscus. B: The top of a convex meniscus. In physics (particularly fluid statics), the meniscus (pl.: menisci, from Greek 'crescent') is the curve in the upper surface of a liquid close to the surface of the container or another object, produced by surface tension.
The following are among the properties of log-concave distributions: If a density is log-concave, so is its cumulative distribution function (CDF). If a multivariate density is log-concave, so is the marginal density over any subset of variables. The sum of two independent log-concave random variables is log-concave. This follows from the fact ...
The term convex is often referred to as convex down or concave upward, and the term concave is often referred as concave down or convex upward. [ 3 ] [ 4 ] [ 5 ] If the term "convex" is used without an "up" or "down" keyword, then it refers strictly to a cup shaped graph ∪ {\displaystyle \cup } .
Thus, the collection of −∞-convex measures is the largest such class, whereas the 0-convex measures (the logarithmically concave measures) are the smallest class. The convexity of a measure μ on n -dimensional Euclidean space R n in the sense above is closely related to the convexity of its probability density function . [ 2 ]
Quasiconvexity is a generalisation of convexity for functions defined on matrices, to see this let and ((,),) with (,) =.The Riesz-Markov-Kakutani representation theorem states that the dual space of () can be identified with the space of signed, finite Radon measures on it.
Convex hull, alpha shape and minimal spanning tree of a bivariate data set. In computational geometry, an alpha shape, or α-shape, is a family of piecewise linear simple curves in the Euclidean plane associated with the shape of a finite set of points. They were first defined by Edelsbrunner, Kirkpatrick & Seidel (1983).