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3.6% (1 in 28) – The Westmere Bank, New Zealand has a ruling gradient of 1 in 35, however peaks at 1 in 28; 3.33% (1 in 30) – Umgeni Steam Railway, South Africa [25] 3.0% (1 in 33) – several sections of the Main Western line between Valley Heights and Katoomba in the Blue Mountains Australia. [26]
The gradient theorem states that if the vector field F is the gradient of some scalar-valued function (i.e., if F is conservative), then F is a path-independent vector field (i.e., the integral of F over some piecewise-differentiable curve is dependent only on end points). This theorem has a powerful converse:
LinkedIn Learning is an American online learning platform. It provides video courses taught by industry experts in software, creative, and business skills. It is a subsidiary of LinkedIn. All the courses on LinkedIn fall into four categories: Business, Creative, Technology, and Certifications.
Gradient descent with momentum remembers the solution update at each iteration, and determines the next update as a linear combination of the gradient and the previous update. For unconstrained quadratic minimization, a theoretical convergence rate bound of the heavy ball method is asymptotically the same as that for the optimal conjugate ...
Exome sequencing, also known as whole exome sequencing (WES), is a genomic technique for sequencing all of the protein-coding regions of genes in a genome (known as the exome). [1] It consists of two steps: the first step is to select only the subset of DNA that encodes proteins .
The conjugate gradient method can also be used to solve unconstrained optimization problems such as energy minimization. It is commonly attributed to Magnus Hestenes and Eduard Stiefel, [1] [2] who programmed it on the Z4, [3] and extensively researched it. [4] [5] The biconjugate gradient method provides a generalization to non-symmetric matrices.
The simplest definition for a potential gradient F in one dimension is the following: [1] = = where ϕ(x) is some type of scalar potential and x is displacement (not distance) in the x direction, the subscripts label two different positions x 1, x 2, and potentials at those points, ϕ 1 = ϕ(x 1), ϕ 2 = ϕ(x 2).
In statistics, the score (or informant [1]) is the gradient of the log-likelihood function with respect to the parameter vector. Evaluated at a particular value of the parameter vector, the score indicates the steepness of the log-likelihood function and thereby the sensitivity to infinitesimal changes to the parameter values.