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Exponential decay. A quantity undergoing exponential decay. Larger decay constants make the quantity vanish much more rapidly. This plot shows decay for decay constant (λ) of 25, 5, 1, 1/5, and 1/25 for x from 0 to 5. A quantity is subject to exponential decay if it decreases at a rate proportional to its current value.
In statistics, a power law is a functional relationship between two quantities, where a relative change in one quantity results in a relative change in the other quantity proportional to a power of the change, independent of the initial size of those quantities: one quantity varies as a power of another. For instance, considering the area of a ...
In probability theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the distance between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate; the distance parameter could be any meaningful mono-dimensional measure of the process, such as time ...
In stochastic (or "on-line") gradient descent, the true gradient of is approximated by a gradient at a single sample: As the algorithm sweeps through the training set, it performs the above update for each training sample. Several passes can be made over the training set until the algorithm converges.
Fluorescence-lifetime imaging microscopy. Fluorescence-lifetime imaging microscopy or FLIM is an imaging technique based on the differences in the exponential decay rate of the photon emission of a fluorophore from a sample. It can be used as an imaging technique in confocal microscopy, two-photon excitation microscopy, and multiphoton tomography.
Generally, WKB theory is a method for approximating the solution of a differential equation whose highest derivative is multiplied by a small parameter ε. The method of approximation is as follows. For a differential equation assume a solution of the form of an asymptotic series expansion in the limit δ → 0. The asymptotic scaling of δ in ...
The stretched exponential function is obtained by inserting a fractional power law into the exponential function. In most applications, it is meaningful only for arguments t between 0 and +∞. With β = 1, the usual exponential function is recovered. With a stretching exponent β between 0 and 1, the graph of log f versus t is ...
The sample covariance matrix (SCM) is an unbiased and efficient estimator of the covariance matrix if the space of covariance matrices is viewed as an extrinsic convex cone in Rp×p; however, measured using the intrinsic geometry of positive-definite matrices, the SCM is a biased and inefficient estimator. [1]