Concepts inAn algebraic spline model of molecular surfaces
Accessible surface area
The accessible surface area (ASA) or solvent-accessible surface area (SASA) is the surface area of a biomolecule that is accessible to a solvent. Measurement of ASA is usually described in units of square ångstroms. ASA was first described by Lee & Richards in 1971 and is sometimes called the Lee-Richards molecular surface. ASA is typically calculated using the 'rolling ball' algorithm developed by Shrake & Rupley in 1973.
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Spline (mathematics)
In mathematics, a spline is a sufficiently smooth polynomial function that is piecewise-defined, and possesses a high degree of smoothness at the places where the polynomial pieces connect (which are known as knots). In interpolating problems, spline interpolation is often referred to as polynomial interpolation because it yields similar results, even when using low-degree polynomials, while avoiding Runge's phenomenon for higher degrees.
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Algebraic geometry
Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex analysis, topology and number theory.
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Model theory
In mathematics, model theory is the study of (classes of) mathematical structures using tools from mathematical logic. It has close ties to abstract algebra, particularly universal algebra. Objects of study in model theory are models for formal languages which are structures that give meaning to the sentences of these formal languages.
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Implicit and explicit functions
The implicit function theorem provides a link between implicit and explicit functions. It states that if the equation R(x, y) = 0 satisfies some mild conditions on its partial derivatives, then one can in principle solve this equation for y, at least over some small interval. Geometrically, the graph defined by R(x,y) = 0 will overlap locally with the graph of an equation y = f(x).
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Nearest-neighbor interpolation
Nearest-neighbor interpolation (also known as proximal interpolation or, in some contexts, point sampling) is a simple method of multivariate interpolation in one or more dimensions. Interpolation is the problem of approximating the value for a non-given point in some space when given some colors of points around (neighboring) that point.
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Piecewise
In mathematics, a piecewise-defined function (also called a piecewise function) is a function whose definition changes depending on the value of the independent variable. Mathematically, a real-valued function f of a real variable x is a relationship whose definition is given differently on disjoint subsets of its domain (known as subdomains).
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Approximation error
The approximation error in some data is the discrepancy between an exact value and some approximation to it. An approximation error can occur because the measurement of the data is not precise due to the instruments. (e.g. , the accurate reading of a piece of paper is 4.5cm but since the ruler does not use decimals, you round it to 5cm. ) or approximations are used instead of the real data (e.g. , 3.14 instead of ¿).
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